SlideShare a Scribd company logo
Given that T is unitary
|T| = 1
|I-ieH| =1
det (-T) = (-1)ndet T
Hence det (ieH-1) = (-1)n
det ieH = 1+(-1)n
i.e. det ieH can be either 0 or 2
To prove that H is equal to its own conjugate transpose
Solution
Given that T is unitary
|T| = 1
|I-ieH| =1
det (-T) = (-1)ndet T
Hence det (ieH-1) = (-1)n
det ieH = 1+(-1)n
i.e. det ieH can be either 0 or 2
To prove that H is equal to its own conjugate transpose

More Related Content

More from ANSAPPARELS

The most critical shortcomings of these assumptions are1.The flow .pdf
The most critical shortcomings of these assumptions are1.The flow .pdfThe most critical shortcomings of these assumptions are1.The flow .pdf
The most critical shortcomings of these assumptions are1.The flow .pdf
ANSAPPARELS
 
The following statements are true1. The tendency of water to mini.pdf
The following statements are true1. The tendency of water to mini.pdfThe following statements are true1. The tendency of water to mini.pdf
The following statements are true1. The tendency of water to mini.pdf
ANSAPPARELS
 
The data is Quantitative as there are numbers , and its an observati.pdf
The data is Quantitative as there are numbers , and its an observati.pdfThe data is Quantitative as there are numbers , and its an observati.pdf
The data is Quantitative as there are numbers , and its an observati.pdf
ANSAPPARELS
 
Thank you everyone! The answer was O(n!)SolutionThank you ever.pdf
Thank you everyone! The answer was O(n!)SolutionThank you ever.pdfThank you everyone! The answer was O(n!)SolutionThank you ever.pdf
Thank you everyone! The answer was O(n!)SolutionThank you ever.pdf
ANSAPPARELS
 
Solution1 ) The purpose of criminal law is to help maintain social.pdf
Solution1 ) The purpose of criminal law is to help maintain social.pdfSolution1 ) The purpose of criminal law is to help maintain social.pdf
Solution1 ) The purpose of criminal law is to help maintain social.pdf
ANSAPPARELS
 
question not visibleSolutionquestion not visible.pdf
question not visibleSolutionquestion not visible.pdfquestion not visibleSolutionquestion not visible.pdf
question not visibleSolutionquestion not visible.pdf
ANSAPPARELS
 
num.txt(Save this file under D Drive.Then the path of the file is D.pdf
num.txt(Save this file under D Drive.Then the path of the file is D.pdfnum.txt(Save this file under D Drive.Then the path of the file is D.pdf
num.txt(Save this file under D Drive.Then the path of the file is D.pdf
ANSAPPARELS
 
n = 7 which is odd so median is the middle value of te data after ar.pdf
n = 7 which is odd so median is the middle value of te data after ar.pdfn = 7 which is odd so median is the middle value of te data after ar.pdf
n = 7 which is odd so median is the middle value of te data after ar.pdf
ANSAPPARELS
 
Molybdenum is the elementSolutionMolybdenum is the element.pdf
Molybdenum is the elementSolutionMolybdenum is the element.pdfMolybdenum is the elementSolutionMolybdenum is the element.pdf
Molybdenum is the elementSolutionMolybdenum is the element.pdf
ANSAPPARELS
 
Mean absolute deviationSolutionMean absolute deviation.pdf
Mean absolute deviationSolutionMean absolute deviation.pdfMean absolute deviationSolutionMean absolute deviation.pdf
Mean absolute deviationSolutionMean absolute deviation.pdf
ANSAPPARELS
 
elements involved are C and N .pdf
                     elements involved are C and N                    .pdf                     elements involved are C and N                    .pdf
elements involved are C and N .pdf
ANSAPPARELS
 
Information security means protecting information (data) and informa.pdf
Information security means protecting information (data) and informa.pdfInformation security means protecting information (data) and informa.pdf
Information security means protecting information (data) and informa.pdf
ANSAPPARELS
 
Gene expressionGene expression is the process by which the genetic.pdf
Gene expressionGene expression is the process by which the genetic.pdfGene expressionGene expression is the process by which the genetic.pdf
Gene expressionGene expression is the process by which the genetic.pdf
ANSAPPARELS
 
Dysfunctional intercellular communication may result in various cond.pdf
Dysfunctional intercellular communication may result in various cond.pdfDysfunctional intercellular communication may result in various cond.pdf
Dysfunctional intercellular communication may result in various cond.pdf
ANSAPPARELS
 
Dear,The answer is 2.SolutionDear,The answer is 2..pdf
Dear,The answer is 2.SolutionDear,The answer is 2..pdfDear,The answer is 2.SolutionDear,The answer is 2..pdf
Dear,The answer is 2.SolutionDear,The answer is 2..pdf
ANSAPPARELS
 
Correcty option. C. PhenotypeThe visible expressions (traits or ch.pdf
Correcty option. C. PhenotypeThe visible expressions (traits or ch.pdfCorrecty option. C. PhenotypeThe visible expressions (traits or ch.pdf
Correcty option. C. PhenotypeThe visible expressions (traits or ch.pdf
ANSAPPARELS
 
Code public class program2 { public static void main(String.pdf
Code public class program2 { public static void main(String.pdfCode public class program2 { public static void main(String.pdf
Code public class program2 { public static void main(String.pdf
ANSAPPARELS
 
can you write the questionsSolutioncan you write the questio.pdf
can you write the questionsSolutioncan you write the questio.pdfcan you write the questionsSolutioncan you write the questio.pdf
can you write the questionsSolutioncan you write the questio.pdf
ANSAPPARELS
 
C. If you haven’t partitioned and formatted the hard disk before ins.pdf
C. If you haven’t partitioned and formatted the hard disk before ins.pdfC. If you haven’t partitioned and formatted the hard disk before ins.pdf
C. If you haven’t partitioned and formatted the hard disk before ins.pdf
ANSAPPARELS
 
bicoid is a transcription factor, so it must bind to the caudal prom.pdf
bicoid is a transcription factor, so it must bind to the caudal prom.pdfbicoid is a transcription factor, so it must bind to the caudal prom.pdf
bicoid is a transcription factor, so it must bind to the caudal prom.pdf
ANSAPPARELS
 

More from ANSAPPARELS (20)

The most critical shortcomings of these assumptions are1.The flow .pdf
The most critical shortcomings of these assumptions are1.The flow .pdfThe most critical shortcomings of these assumptions are1.The flow .pdf
The most critical shortcomings of these assumptions are1.The flow .pdf
 
The following statements are true1. The tendency of water to mini.pdf
The following statements are true1. The tendency of water to mini.pdfThe following statements are true1. The tendency of water to mini.pdf
The following statements are true1. The tendency of water to mini.pdf
 
The data is Quantitative as there are numbers , and its an observati.pdf
The data is Quantitative as there are numbers , and its an observati.pdfThe data is Quantitative as there are numbers , and its an observati.pdf
The data is Quantitative as there are numbers , and its an observati.pdf
 
Thank you everyone! The answer was O(n!)SolutionThank you ever.pdf
Thank you everyone! The answer was O(n!)SolutionThank you ever.pdfThank you everyone! The answer was O(n!)SolutionThank you ever.pdf
Thank you everyone! The answer was O(n!)SolutionThank you ever.pdf
 
Solution1 ) The purpose of criminal law is to help maintain social.pdf
Solution1 ) The purpose of criminal law is to help maintain social.pdfSolution1 ) The purpose of criminal law is to help maintain social.pdf
Solution1 ) The purpose of criminal law is to help maintain social.pdf
 
question not visibleSolutionquestion not visible.pdf
question not visibleSolutionquestion not visible.pdfquestion not visibleSolutionquestion not visible.pdf
question not visibleSolutionquestion not visible.pdf
 
num.txt(Save this file under D Drive.Then the path of the file is D.pdf
num.txt(Save this file under D Drive.Then the path of the file is D.pdfnum.txt(Save this file under D Drive.Then the path of the file is D.pdf
num.txt(Save this file under D Drive.Then the path of the file is D.pdf
 
n = 7 which is odd so median is the middle value of te data after ar.pdf
n = 7 which is odd so median is the middle value of te data after ar.pdfn = 7 which is odd so median is the middle value of te data after ar.pdf
n = 7 which is odd so median is the middle value of te data after ar.pdf
 
Molybdenum is the elementSolutionMolybdenum is the element.pdf
Molybdenum is the elementSolutionMolybdenum is the element.pdfMolybdenum is the elementSolutionMolybdenum is the element.pdf
Molybdenum is the elementSolutionMolybdenum is the element.pdf
 
Mean absolute deviationSolutionMean absolute deviation.pdf
Mean absolute deviationSolutionMean absolute deviation.pdfMean absolute deviationSolutionMean absolute deviation.pdf
Mean absolute deviationSolutionMean absolute deviation.pdf
 
elements involved are C and N .pdf
                     elements involved are C and N                    .pdf                     elements involved are C and N                    .pdf
elements involved are C and N .pdf
 
Information security means protecting information (data) and informa.pdf
Information security means protecting information (data) and informa.pdfInformation security means protecting information (data) and informa.pdf
Information security means protecting information (data) and informa.pdf
 
Gene expressionGene expression is the process by which the genetic.pdf
Gene expressionGene expression is the process by which the genetic.pdfGene expressionGene expression is the process by which the genetic.pdf
Gene expressionGene expression is the process by which the genetic.pdf
 
Dysfunctional intercellular communication may result in various cond.pdf
Dysfunctional intercellular communication may result in various cond.pdfDysfunctional intercellular communication may result in various cond.pdf
Dysfunctional intercellular communication may result in various cond.pdf
 
Dear,The answer is 2.SolutionDear,The answer is 2..pdf
Dear,The answer is 2.SolutionDear,The answer is 2..pdfDear,The answer is 2.SolutionDear,The answer is 2..pdf
Dear,The answer is 2.SolutionDear,The answer is 2..pdf
 
Correcty option. C. PhenotypeThe visible expressions (traits or ch.pdf
Correcty option. C. PhenotypeThe visible expressions (traits or ch.pdfCorrecty option. C. PhenotypeThe visible expressions (traits or ch.pdf
Correcty option. C. PhenotypeThe visible expressions (traits or ch.pdf
 
Code public class program2 { public static void main(String.pdf
Code public class program2 { public static void main(String.pdfCode public class program2 { public static void main(String.pdf
Code public class program2 { public static void main(String.pdf
 
can you write the questionsSolutioncan you write the questio.pdf
can you write the questionsSolutioncan you write the questio.pdfcan you write the questionsSolutioncan you write the questio.pdf
can you write the questionsSolutioncan you write the questio.pdf
 
C. If you haven’t partitioned and formatted the hard disk before ins.pdf
C. If you haven’t partitioned and formatted the hard disk before ins.pdfC. If you haven’t partitioned and formatted the hard disk before ins.pdf
C. If you haven’t partitioned and formatted the hard disk before ins.pdf
 
bicoid is a transcription factor, so it must bind to the caudal prom.pdf
bicoid is a transcription factor, so it must bind to the caudal prom.pdfbicoid is a transcription factor, so it must bind to the caudal prom.pdf
bicoid is a transcription factor, so it must bind to the caudal prom.pdf
 

Recently uploaded

Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
Thiyagu K
 
The Accursed House by Émile Gaboriau.pptx
The Accursed House by Émile Gaboriau.pptxThe Accursed House by Émile Gaboriau.pptx
The Accursed House by Émile Gaboriau.pptx
DhatriParmar
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
Pavel ( NSTU)
 
Francesca Gottschalk - How can education support child empowerment.pptx
Francesca Gottschalk - How can education support child empowerment.pptxFrancesca Gottschalk - How can education support child empowerment.pptx
Francesca Gottschalk - How can education support child empowerment.pptx
EduSkills OECD
 
A Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in EducationA Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in Education
Peter Windle
 
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School DistrictPride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
David Douglas School District
 
Multithreading_in_C++ - std::thread, race condition
Multithreading_in_C++ - std::thread, race conditionMultithreading_in_C++ - std::thread, race condition
Multithreading_in_C++ - std::thread, race condition
Mohammed Sikander
 
"Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe..."Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe...
SACHIN R KONDAGURI
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
Balvir Singh
 
Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp NetworkIntroduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
TechSoup
 
Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
Jean Carlos Nunes Paixão
 
BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...
BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...
BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...
Nguyen Thanh Tu Collection
 
The basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptxThe basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptx
heathfieldcps1
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
Special education needs
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
JosvitaDsouza2
 
Best Digital Marketing Institute In NOIDA
Best Digital Marketing Institute In NOIDABest Digital Marketing Institute In NOIDA
Best Digital Marketing Institute In NOIDA
deeptiverma2406
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
Levi Shapiro
 
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdfMASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
goswamiyash170123
 
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
Academy of Science of South Africa
 

Recently uploaded (20)

Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
 
The Accursed House by Émile Gaboriau.pptx
The Accursed House by Émile Gaboriau.pptxThe Accursed House by Émile Gaboriau.pptx
The Accursed House by Émile Gaboriau.pptx
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
 
Francesca Gottschalk - How can education support child empowerment.pptx
Francesca Gottschalk - How can education support child empowerment.pptxFrancesca Gottschalk - How can education support child empowerment.pptx
Francesca Gottschalk - How can education support child empowerment.pptx
 
A Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in EducationA Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in Education
 
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School DistrictPride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
 
Multithreading_in_C++ - std::thread, race condition
Multithreading_in_C++ - std::thread, race conditionMultithreading_in_C++ - std::thread, race condition
Multithreading_in_C++ - std::thread, race condition
 
"Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe..."Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe...
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
 
Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp NetworkIntroduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
 
Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
 
BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...
BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...
BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...
 
The basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptxThe basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptx
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
 
Best Digital Marketing Institute In NOIDA
Best Digital Marketing Institute In NOIDABest Digital Marketing Institute In NOIDA
Best Digital Marketing Institute In NOIDA
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
 
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdfMASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
 
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
 

Given that T is unitaryT = 1I-ieH =1det (-T) = (-1)ndet T.pdf

  • 1. Given that T is unitary |T| = 1 |I-ieH| =1 det (-T) = (-1)ndet T Hence det (ieH-1) = (-1)n det ieH = 1+(-1)n i.e. det ieH can be either 0 or 2 To prove that H is equal to its own conjugate transpose Solution Given that T is unitary |T| = 1 |I-ieH| =1 det (-T) = (-1)ndet T Hence det (ieH-1) = (-1)n det ieH = 1+(-1)n i.e. det ieH can be either 0 or 2 To prove that H is equal to its own conjugate transpose