SlideShare a Scribd company logo
1 of 39
LINEAR ALGEBRA
By
Dr. R. Kalaivanan
UNIT - IV
(Remaining Portion)
UNIT - V
BILINEAR
Quadratic Form
Arise! Awake! and stop not until the goal is reached.
Swami Vivekananda

More Related Content

Recently uploaded

ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...JojoEDelaCruz
 
ICS2208 Lecture6 Notes for SL spaces.pdf
ICS2208 Lecture6 Notes for SL spaces.pdfICS2208 Lecture6 Notes for SL spaces.pdf
ICS2208 Lecture6 Notes for SL spaces.pdfVanessa Camilleri
 
EMBODO Lesson Plan Grade 9 Law of Sines.docx
EMBODO Lesson Plan Grade 9 Law of Sines.docxEMBODO Lesson Plan Grade 9 Law of Sines.docx
EMBODO Lesson Plan Grade 9 Law of Sines.docxElton John Embodo
 
Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4JOYLYNSAMANIEGO
 
AUDIENCE THEORY -CULTIVATION THEORY - GERBNER.pptx
AUDIENCE THEORY -CULTIVATION THEORY -  GERBNER.pptxAUDIENCE THEORY -CULTIVATION THEORY -  GERBNER.pptx
AUDIENCE THEORY -CULTIVATION THEORY - GERBNER.pptxiammrhaywood
 
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17Celine George
 
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)lakshayb543
 
ROLES IN A STAGE PRODUCTION in arts.pptx
ROLES IN A STAGE PRODUCTION in arts.pptxROLES IN A STAGE PRODUCTION in arts.pptx
ROLES IN A STAGE PRODUCTION in arts.pptxVanesaIglesias10
 
Choosing the Right CBSE School A Comprehensive Guide for Parents
Choosing the Right CBSE School A Comprehensive Guide for ParentsChoosing the Right CBSE School A Comprehensive Guide for Parents
Choosing the Right CBSE School A Comprehensive Guide for Parentsnavabharathschool99
 
Expanded definition: technical and operational
Expanded definition: technical and operationalExpanded definition: technical and operational
Expanded definition: technical and operationalssuser3e220a
 
Active Learning Strategies (in short ALS).pdf
Active Learning Strategies (in short ALS).pdfActive Learning Strategies (in short ALS).pdf
Active Learning Strategies (in short ALS).pdfPatidar M
 
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxQ4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxlancelewisportillo
 
4.18.24 Movement Legacies, Reflection, and Review.pptx
4.18.24 Movement Legacies, Reflection, and Review.pptx4.18.24 Movement Legacies, Reflection, and Review.pptx
4.18.24 Movement Legacies, Reflection, and Review.pptxmary850239
 
4.16.24 21st Century Movements for Black Lives.pptx
4.16.24 21st Century Movements for Black Lives.pptx4.16.24 21st Century Movements for Black Lives.pptx
4.16.24 21st Century Movements for Black Lives.pptxmary850239
 
USPS® Forced Meter Migration - How to Know if Your Postage Meter Will Soon be...
USPS® Forced Meter Migration - How to Know if Your Postage Meter Will Soon be...USPS® Forced Meter Migration - How to Know if Your Postage Meter Will Soon be...
USPS® Forced Meter Migration - How to Know if Your Postage Meter Will Soon be...Postal Advocate Inc.
 
INTRODUCTION TO CATHOLIC CHRISTOLOGY.pptx
INTRODUCTION TO CATHOLIC CHRISTOLOGY.pptxINTRODUCTION TO CATHOLIC CHRISTOLOGY.pptx
INTRODUCTION TO CATHOLIC CHRISTOLOGY.pptxHumphrey A Beña
 
TEACHER REFLECTION FORM (NEW SET........).docx
TEACHER REFLECTION FORM (NEW SET........).docxTEACHER REFLECTION FORM (NEW SET........).docx
TEACHER REFLECTION FORM (NEW SET........).docxruthvilladarez
 

Recently uploaded (20)

ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
 
ICS2208 Lecture6 Notes for SL spaces.pdf
ICS2208 Lecture6 Notes for SL spaces.pdfICS2208 Lecture6 Notes for SL spaces.pdf
ICS2208 Lecture6 Notes for SL spaces.pdf
 
EMBODO Lesson Plan Grade 9 Law of Sines.docx
EMBODO Lesson Plan Grade 9 Law of Sines.docxEMBODO Lesson Plan Grade 9 Law of Sines.docx
EMBODO Lesson Plan Grade 9 Law of Sines.docx
 
Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4
 
AUDIENCE THEORY -CULTIVATION THEORY - GERBNER.pptx
AUDIENCE THEORY -CULTIVATION THEORY -  GERBNER.pptxAUDIENCE THEORY -CULTIVATION THEORY -  GERBNER.pptx
AUDIENCE THEORY -CULTIVATION THEORY - GERBNER.pptx
 
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
 
Paradigm shift in nursing research by RS MEHTA
Paradigm shift in nursing research by RS MEHTAParadigm shift in nursing research by RS MEHTA
Paradigm shift in nursing research by RS MEHTA
 
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
 
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptxYOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
 
ROLES IN A STAGE PRODUCTION in arts.pptx
ROLES IN A STAGE PRODUCTION in arts.pptxROLES IN A STAGE PRODUCTION in arts.pptx
ROLES IN A STAGE PRODUCTION in arts.pptx
 
Choosing the Right CBSE School A Comprehensive Guide for Parents
Choosing the Right CBSE School A Comprehensive Guide for ParentsChoosing the Right CBSE School A Comprehensive Guide for Parents
Choosing the Right CBSE School A Comprehensive Guide for Parents
 
Expanded definition: technical and operational
Expanded definition: technical and operationalExpanded definition: technical and operational
Expanded definition: technical and operational
 
Active Learning Strategies (in short ALS).pdf
Active Learning Strategies (in short ALS).pdfActive Learning Strategies (in short ALS).pdf
Active Learning Strategies (in short ALS).pdf
 
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxQ4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
 
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptxINCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
 
4.18.24 Movement Legacies, Reflection, and Review.pptx
4.18.24 Movement Legacies, Reflection, and Review.pptx4.18.24 Movement Legacies, Reflection, and Review.pptx
4.18.24 Movement Legacies, Reflection, and Review.pptx
 
4.16.24 21st Century Movements for Black Lives.pptx
4.16.24 21st Century Movements for Black Lives.pptx4.16.24 21st Century Movements for Black Lives.pptx
4.16.24 21st Century Movements for Black Lives.pptx
 
USPS® Forced Meter Migration - How to Know if Your Postage Meter Will Soon be...
USPS® Forced Meter Migration - How to Know if Your Postage Meter Will Soon be...USPS® Forced Meter Migration - How to Know if Your Postage Meter Will Soon be...
USPS® Forced Meter Migration - How to Know if Your Postage Meter Will Soon be...
 
INTRODUCTION TO CATHOLIC CHRISTOLOGY.pptx
INTRODUCTION TO CATHOLIC CHRISTOLOGY.pptxINTRODUCTION TO CATHOLIC CHRISTOLOGY.pptx
INTRODUCTION TO CATHOLIC CHRISTOLOGY.pptx
 
TEACHER REFLECTION FORM (NEW SET........).docx
TEACHER REFLECTION FORM (NEW SET........).docxTEACHER REFLECTION FORM (NEW SET........).docx
TEACHER REFLECTION FORM (NEW SET........).docx
 

Featured

How Race, Age and Gender Shape Attitudes Towards Mental Health
How Race, Age and Gender Shape Attitudes Towards Mental HealthHow Race, Age and Gender Shape Attitudes Towards Mental Health
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
 
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
AI Trends in Creative Operations 2024 by Artwork Flow.pdfAI Trends in Creative Operations 2024 by Artwork Flow.pdf
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
 
PEPSICO Presentation to CAGNY Conference Feb 2024
PEPSICO Presentation to CAGNY Conference Feb 2024PEPSICO Presentation to CAGNY Conference Feb 2024
PEPSICO Presentation to CAGNY Conference Feb 2024Neil Kimberley
 
Content Methodology: A Best Practices Report (Webinar)
Content Methodology: A Best Practices Report (Webinar)Content Methodology: A Best Practices Report (Webinar)
Content Methodology: A Best Practices Report (Webinar)contently
 
How to Prepare For a Successful Job Search for 2024
How to Prepare For a Successful Job Search for 2024How to Prepare For a Successful Job Search for 2024
How to Prepare For a Successful Job Search for 2024Albert Qian
 
Social Media Marketing Trends 2024 // The Global Indie Insights
Social Media Marketing Trends 2024 // The Global Indie InsightsSocial Media Marketing Trends 2024 // The Global Indie Insights
Social Media Marketing Trends 2024 // The Global Indie InsightsKurio // The Social Media Age(ncy)
 
Trends In Paid Search: Navigating The Digital Landscape In 2024
Trends In Paid Search: Navigating The Digital Landscape In 2024Trends In Paid Search: Navigating The Digital Landscape In 2024
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
 
5 Public speaking tips from TED - Visualized summary
5 Public speaking tips from TED - Visualized summary5 Public speaking tips from TED - Visualized summary
5 Public speaking tips from TED - Visualized summarySpeakerHub
 
ChatGPT and the Future of Work - Clark Boyd
ChatGPT and the Future of Work - Clark Boyd ChatGPT and the Future of Work - Clark Boyd
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
 
Getting into the tech field. what next
Getting into the tech field. what next Getting into the tech field. what next
Getting into the tech field. what next Tessa Mero
 
Google's Just Not That Into You: Understanding Core Updates & Search Intent
Google's Just Not That Into You: Understanding Core Updates & Search IntentGoogle's Just Not That Into You: Understanding Core Updates & Search Intent
Google's Just Not That Into You: Understanding Core Updates & Search IntentLily Ray
 
Time Management & Productivity - Best Practices
Time Management & Productivity -  Best PracticesTime Management & Productivity -  Best Practices
Time Management & Productivity - Best PracticesVit Horky
 
The six step guide to practical project management
The six step guide to practical project managementThe six step guide to practical project management
The six step guide to practical project managementMindGenius
 
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...RachelPearson36
 
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...Applitools
 
12 Ways to Increase Your Influence at Work
12 Ways to Increase Your Influence at Work12 Ways to Increase Your Influence at Work
12 Ways to Increase Your Influence at WorkGetSmarter
 

Featured (20)

How Race, Age and Gender Shape Attitudes Towards Mental Health
How Race, Age and Gender Shape Attitudes Towards Mental HealthHow Race, Age and Gender Shape Attitudes Towards Mental Health
How Race, Age and Gender Shape Attitudes Towards Mental Health
 
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
AI Trends in Creative Operations 2024 by Artwork Flow.pdfAI Trends in Creative Operations 2024 by Artwork Flow.pdf
AI Trends in Creative Operations 2024 by Artwork Flow.pdf
 
Skeleton Culture Code
Skeleton Culture CodeSkeleton Culture Code
Skeleton Culture Code
 
PEPSICO Presentation to CAGNY Conference Feb 2024
PEPSICO Presentation to CAGNY Conference Feb 2024PEPSICO Presentation to CAGNY Conference Feb 2024
PEPSICO Presentation to CAGNY Conference Feb 2024
 
Content Methodology: A Best Practices Report (Webinar)
Content Methodology: A Best Practices Report (Webinar)Content Methodology: A Best Practices Report (Webinar)
Content Methodology: A Best Practices Report (Webinar)
 
How to Prepare For a Successful Job Search for 2024
How to Prepare For a Successful Job Search for 2024How to Prepare For a Successful Job Search for 2024
How to Prepare For a Successful Job Search for 2024
 
Social Media Marketing Trends 2024 // The Global Indie Insights
Social Media Marketing Trends 2024 // The Global Indie InsightsSocial Media Marketing Trends 2024 // The Global Indie Insights
Social Media Marketing Trends 2024 // The Global Indie Insights
 
Trends In Paid Search: Navigating The Digital Landscape In 2024
Trends In Paid Search: Navigating The Digital Landscape In 2024Trends In Paid Search: Navigating The Digital Landscape In 2024
Trends In Paid Search: Navigating The Digital Landscape In 2024
 
5 Public speaking tips from TED - Visualized summary
5 Public speaking tips from TED - Visualized summary5 Public speaking tips from TED - Visualized summary
5 Public speaking tips from TED - Visualized summary
 
ChatGPT and the Future of Work - Clark Boyd
ChatGPT and the Future of Work - Clark Boyd ChatGPT and the Future of Work - Clark Boyd
ChatGPT and the Future of Work - Clark Boyd
 
Getting into the tech field. what next
Getting into the tech field. what next Getting into the tech field. what next
Getting into the tech field. what next
 
Google's Just Not That Into You: Understanding Core Updates & Search Intent
Google's Just Not That Into You: Understanding Core Updates & Search IntentGoogle's Just Not That Into You: Understanding Core Updates & Search Intent
Google's Just Not That Into You: Understanding Core Updates & Search Intent
 
How to have difficult conversations
How to have difficult conversations How to have difficult conversations
How to have difficult conversations
 
Introduction to Data Science
Introduction to Data ScienceIntroduction to Data Science
Introduction to Data Science
 
Time Management & Productivity - Best Practices
Time Management & Productivity -  Best PracticesTime Management & Productivity -  Best Practices
Time Management & Productivity - Best Practices
 
The six step guide to practical project management
The six step guide to practical project managementThe six step guide to practical project management
The six step guide to practical project management
 
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
 
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...
 
12 Ways to Increase Your Influence at Work
12 Ways to Increase Your Influence at Work12 Ways to Increase Your Influence at Work
12 Ways to Increase Your Influence at Work
 
ChatGPT webinar slides
ChatGPT webinar slidesChatGPT webinar slides
ChatGPT webinar slides
 

Linear algebra