Diagonalization matrix

•Download as PPTX, PDF•

0 likes•387 views

Diagonalization matrix memo

Diagonalization matrix
Monday March 28 2016
Hanpen Robot

Let 𝔸 be a 2x2 square matrix
and 𝕧 𝜆1
, 𝕧 𝜆2
be a eigenvector of 𝔸.
Now consider a coordinate on 𝕧 𝜆1
, 𝕧 𝜆2
.
𝔸 𝑥𝕧 𝜆1
+ 𝑦𝕧 𝜆2
= 𝑥𝜆1 𝕧 𝜆1
+ 𝑦𝜆2 𝕧 𝜆2
∴
𝑥
𝑦 =
𝜆1 𝑥
𝜆2 𝑦
=
𝜆1 0
0 𝜆2
𝑥
𝑦

Diagonalization matrix

More Related Content

Viewers also liked

Cheat Sheetguest742ba8

Maths-->>Eigenvalues and eigenvectors

Maths-->>Eigenvalues and eigenvectors

Maths-->>Eigenvalues and eigenvectorsJaydev Kishnani

Dsp U Lec05 The Z Transform

Dsp U Lec05 The Z Transform

Dsp U Lec05 The Z Transformtaha25

Discriminant analysis

Discriminant analysis

Discriminant analysisTehran University of Medical Sciences,Tehran, Iran.

Probability Formula sheet

Probability Formula sheet

Probability Formula sheetHaris Hassan

matrices and algbra

matrices and algbra

matrices and algbragandhinagar

Z transformayushagrawal464

Linear Algebra and Matrix

Linear Algebra and Matrix

Linear Algebra and Matrixitutor

Building Compatible Bases on Graphs, Images, and Manifolds

Building Compatible Bases on Graphs, Images, and Manifolds

Building Compatible Bases on Graphs, Images, and ManifoldsDavide Eynard

Viewers also liked (9)

Cheat Sheet

Maths-->>Eigenvalues and eigenvectors

Maths-->>Eigenvalues and eigenvectors

Maths-->>Eigenvalues and eigenvectors

Dsp U Lec05 The Z Transform

Dsp U Lec05 The Z Transform

Dsp U Lec05 The Z Transform

Discriminant analysis

Discriminant analysis

Discriminant analysis

Probability Formula sheet

Probability Formula sheet

Probability Formula sheet

matrices and algbra

matrices and algbra

matrices and algbra

Z transform

Linear Algebra and Matrix

Linear Algebra and Matrix

Linear Algebra and Matrix

Building Compatible Bases on Graphs, Images, and Manifolds

Building Compatible Bases on Graphs, Images, and Manifolds

Building Compatible Bases on Graphs, Images, and Manifolds

More from HanpenRobot

fermat's little theorem and …

fermat's little theorem and …

fermat's little theorem and …HanpenRobot

Campbell hasudorff formula

Campbell hasudorff formula

Campbell hasudorff formulaHanpenRobot

構造定数が随伴表現になることの証明

構造定数が随伴表現になることの証明

構造定数が随伴表現になることの証明HanpenRobot

Log complexHanpenRobot

代数幾何memo_2020March30_1337

代数幾何memo_2020March30_1337

代数幾何memo_2020March30_1337HanpenRobot

金利スワップのメモHanpenRobot

Conditional expectation projection 2018 feb 18

Conditional expectation projection 2018 feb 18

Conditional expectation projection 2018 feb 18 HanpenRobot

集合の上極限，下極限HanpenRobot

確率微分方程式の基礎 HanpenRobot

Noether環上の有限生成加群の有限表示

Noether環上の有限生成加群の有限表示

Noether環上の有限生成加群の有限表示HanpenRobot

微分演算子と多項式の剰余環の関係 2016 october 12

微分演算子と多項式の剰余環の関係 2016 october 12

微分演算子と多項式の剰余環の関係 2016 october 12HanpenRobot

位相空間の開集合の成す圏 2016 august 30

位相空間の開集合の成す圏 2016 august 30

位相空間の開集合の成す圏 2016 august 30HanpenRobot

Fourier transform on real-valued function over symmetric group

Fourier transform on real-valued function over symmetric group

Fourier transform on real-valued function over symmetric groupHanpenRobot

置換族の一様分布HanpenRobot

Duality of laplace transform

Duality of laplace transform

Duality of laplace transformHanpenRobot

Fourier analysis on symmetric group

Fourier analysis on symmetric group

Fourier analysis on symmetric groupHanpenRobot

Conjugate cyclic permutation

Conjugate cyclic permutation

Conjugate cyclic permutationHanpenRobot

ベイズ識別一般化逆行列HanpenRobot

電子光波MemoHanpenRobot

Minimize quadratic form

Minimize quadratic form

Minimize quadratic formHanpenRobot

More from HanpenRobot (20)

fermat's little theorem and …

fermat's little theorem and …

fermat's little theorem and …

Campbell hasudorff formula

Campbell hasudorff formula

Campbell hasudorff formula

構造定数が随伴表現になることの証明

構造定数が随伴表現になることの証明

構造定数が随伴表現になることの証明

Log complex

代数幾何memo_2020March30_1337

代数幾何memo_2020March30_1337

代数幾何memo_2020March30_1337

金利スワップのメモ

Conditional expectation projection 2018 feb 18

Conditional expectation projection 2018 feb 18

Conditional expectation projection 2018 feb 18

集合の上極限，下極限

確率微分方程式の基礎

Noether環上の有限生成加群の有限表示

Noether環上の有限生成加群の有限表示

Noether環上の有限生成加群の有限表示

微分演算子と多項式の剰余環の関係 2016 october 12

微分演算子と多項式の剰余環の関係 2016 october 12

微分演算子と多項式の剰余環の関係 2016 october 12

位相空間の開集合の成す圏 2016 august 30

位相空間の開集合の成す圏 2016 august 30

位相空間の開集合の成す圏 2016 august 30

Fourier transform on real-valued function over symmetric group

Fourier transform on real-valued function over symmetric group

Fourier transform on real-valued function over symmetric group

置換族の一様分布

Duality of laplace transform

Duality of laplace transform

Duality of laplace transform

Fourier analysis on symmetric group

Fourier analysis on symmetric group

Fourier analysis on symmetric group

Conjugate cyclic permutation

Conjugate cyclic permutation

Conjugate cyclic permutation

ベイズ識別一般化逆行列

電子光波Memo

Minimize quadratic form

Minimize quadratic form

Minimize quadratic form

Recently uploaded

Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx

Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx

Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptxRoyAbrique

Class 11 Legal Studies Ch-1 Concept of State .pdf

Class 11 Legal Studies Ch-1 Concept of State .pdf

Class 11 Legal Studies Ch-1 Concept of State .pdfakmcokerachita

mini mental status format.docx

mini mental status format.docx

mini mental status format.docxPoojaSen20

Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝

Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝

Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝9953056974 Low Rate Call Girls In Saket, Delhi NCR

The Most Excellent Way | 1 Corinthians 13

The Most Excellent Way | 1 Corinthians 13

The Most Excellent Way | 1 Corinthians 13Steve Thomason

Incoming and Outgoing Shipments in 1 STEP Using Odoo 17

Incoming and Outgoing Shipments in 1 STEP Using Odoo 17

Incoming and Outgoing Shipments in 1 STEP Using Odoo 17Celine George

Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...

Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...

Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Krashi Coaching

How to Configure Email Server in Odoo 17

How to Configure Email Server in Odoo 17

How to Configure Email Server in Odoo 17Celine George

How to Make a Pirate ship Primary Education.pptx

How to Make a Pirate ship Primary Education.pptx

How to Make a Pirate ship Primary Education.pptxmanuelaromero2013

SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx

SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx

SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptxiammrhaywood

A Critique of the Proposed National Education Policy Reform

A Critique of the Proposed National Education Policy Reform

A Critique of the Proposed National Education Policy ReformChameera Dedduwage

Separation of Lanthanides/ Lanthanides and Actinides

Separation of Lanthanides/ Lanthanides and Actinides

Separation of Lanthanides/ Lanthanides and ActinidesFatimaKhan178732

ECONOMIC CONTEXT - LONG FORM TV DRAMA - PPT

ECONOMIC CONTEXT - LONG FORM TV DRAMA - PPT

ECONOMIC CONTEXT - LONG FORM TV DRAMA - PPTiammrhaywood

BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf

BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf

BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdfSoniaTolstoy

Interactive Powerpoint_How to Master effective communication

Interactive Powerpoint_How to Master effective communication

Interactive Powerpoint_How to Master effective communicationnomboosow

call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️

call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️

call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️9953056974 Low Rate Call Girls In Saket, Delhi NCR

Software Engineering Methodologies (overview)

Software Engineering Methodologies (overview)

Software Engineering Methodologies (overview)eniolaolutunde

Staff of Color (SOC) Retention Efforts DDSD

Staff of Color (SOC) Retention Efforts DDSD

Staff of Color (SOC) Retention Efforts DDSDDavid Douglas School District

Science 7 - LAND and SEA BREEZE and its Characteristics

Science 7 - LAND and SEA BREEZE and its Characteristics

Science 7 - LAND and SEA BREEZE and its CharacteristicsKarinaGenton

CARE OF CHILD IN INCUBATOR..........pptx

CARE OF CHILD IN INCUBATOR..........pptx

CARE OF CHILD IN INCUBATOR..........pptxGaneshChakor2

Recently uploaded (20)

Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx

Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx

Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx

Class 11 Legal Studies Ch-1 Concept of State .pdf

Class 11 Legal Studies Ch-1 Concept of State .pdf

Class 11 Legal Studies Ch-1 Concept of State .pdf

mini mental status format.docx

mini mental status format.docx

mini mental status format.docx

Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝

Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝

Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝

The Most Excellent Way | 1 Corinthians 13

The Most Excellent Way | 1 Corinthians 13

The Most Excellent Way | 1 Corinthians 13

Incoming and Outgoing Shipments in 1 STEP Using Odoo 17

Incoming and Outgoing Shipments in 1 STEP Using Odoo 17

Incoming and Outgoing Shipments in 1 STEP Using Odoo 17

Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...

Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...

Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...

How to Configure Email Server in Odoo 17

How to Configure Email Server in Odoo 17

How to Configure Email Server in Odoo 17

How to Make a Pirate ship Primary Education.pptx

How to Make a Pirate ship Primary Education.pptx

How to Make a Pirate ship Primary Education.pptx

SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx

SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx

SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx

A Critique of the Proposed National Education Policy Reform

A Critique of the Proposed National Education Policy Reform

A Critique of the Proposed National Education Policy Reform

Separation of Lanthanides/ Lanthanides and Actinides

Separation of Lanthanides/ Lanthanides and Actinides

Separation of Lanthanides/ Lanthanides and Actinides

ECONOMIC CONTEXT - LONG FORM TV DRAMA - PPT

ECONOMIC CONTEXT - LONG FORM TV DRAMA - PPT

ECONOMIC CONTEXT - LONG FORM TV DRAMA - PPT

BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf

BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf

BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf

Interactive Powerpoint_How to Master effective communication

Interactive Powerpoint_How to Master effective communication

Interactive Powerpoint_How to Master effective communication

call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️

call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️

call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️

Software Engineering Methodologies (overview)

Software Engineering Methodologies (overview)

Software Engineering Methodologies (overview)

Staff of Color (SOC) Retention Efforts DDSD

Staff of Color (SOC) Retention Efforts DDSD

Staff of Color (SOC) Retention Efforts DDSD

Science 7 - LAND and SEA BREEZE and its Characteristics

Science 7 - LAND and SEA BREEZE and its Characteristics

Science 7 - LAND and SEA BREEZE and its Characteristics

CARE OF CHILD IN INCUBATOR..........pptx

CARE OF CHILD IN INCUBATOR..........pptx

CARE OF CHILD IN INCUBATOR..........pptx

Diagonalization matrix

1. Diagonalization matrix Monday March 28 2016 Hanpen Robot

2. Let 𝔸 be a 2x2 square matrix and 𝕧 𝜆1 , 𝕧 𝜆2 be a eigenvector of 𝔸. Now consider a coordinate on 𝕧 𝜆1 , 𝕧 𝜆2 . 𝔸 𝑥𝕧 𝜆1 + 𝑦𝕧 𝜆2 = 𝑥𝜆1 𝕧 𝜆1 + 𝑦𝜆2 𝕧 𝜆2 ∴ 𝑥 𝑦 = 𝜆1 𝑥 𝜆2 𝑦 = 𝜆1 0 0 𝜆2 𝑥 𝑦