Example of Rational Canonical Form 1: Single Block

Matrix Theory: Let A be the real matrix [0 -1 1 0 \ 1 0 0 1 \ 0 0 0 -1 \ 0 0 1 0]. Find a matrix P that puts A into rational canonical form over the real numbers. We compare RCF with Jordan canonical form and review companion matrices. (Minor corrections added.)

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Example of Rational Canonical Form 2: Several Blocks
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Example of Rational Canonical Form 2: Several Blocks

Example of Rational Canonical Form 3
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Example of Rational Canonical Form 3

25. Symmetric Matrices and Positive Definiteness
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25. Symmetric Matrices and Positive Definiteness

Example of Jordan Canonical Form: General Properties
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Example of Jordan Canonical Form: General Properties

Advanced Linear Algebra 25: Jordan Decomposition Generalized Eigenspace
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Advanced Linear Algebra 25: Jordan Decomposition Generalized Eigenspace

21. Eigenvalues and Eigenvectors
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21. Eigenvalues and Eigenvectors

We're 99.9% sure this pattern is true, but no one can prove it
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We're 99.9% sure this pattern is true, but no one can prove it

Overview of Jordan Canonical Form
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Overview of Jordan Canonical Form

Watch Ukrainian Drones OBLITERATE a Russian Jet
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Watch Ukrainian Drones OBLITERATE a Russian Jet

If You Have A Bad Memory, I’ll Help You Fix It In 28 Minutes
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If You Have A Bad Memory, I’ll Help You Fix It In 28 Minutes

You Know This Song (but the Orchestra Doesn’t) | Jacob Collier & VSO School of Music Orchestra | TED
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You Know This Song (but the Orchestra Doesn’t) | Jacob Collier & VSO School of Music Orchestra | TED

Linear Algebra: 049 Invariant Factors, Rational Canonical Forms
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Linear Algebra: 049 Invariant Factors, Rational Canonical Forms

See How a 453kg Giant Bluefin Tuna Is Flawlessly Carved in Seconds
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See How a 453kg Giant Bluefin Tuna Is Flawlessly Carved in Seconds

Jordan Canonical Form
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Jordan Canonical Form

Train Your Brain to Never Forget (5 Feynman Habits)
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Train Your Brain to Never Forget (5 Feynman Habits)

Professor Jiang: World War 3 Is About To Begin, Let Me Explain!
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Professor Jiang: World War 3 Is About To Begin, Let Me Explain!

Overview of Minimal Polynomials
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Overview of Minimal Polynomials

The Oldest Unsolved Problem in Math
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The Oldest Unsolved Problem in Math

F[x]-Module Derivation of Rational and Jordan Canonical Forms
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F[x]-Module Derivation of Rational and Jordan Canonical Forms

But what is the Central Limit Theorem?
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But what is the Central Limit Theorem?