Matrix theory | Matrices

Companion matrix

In linear algebra, the Frobenius companion matrix of the monic polynomial is the square matrix defined as . Some authors use the transpose of this matrix, which (dually) cycles coordinates, and is more convenient for some purposes, like linear recurrence relations. (Wikipedia).

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What is a Matrix?

What is a matrix? Free ebook http://tinyurl.com/EngMathYT

From playlist Intro to Matrices

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2 Construction of a Matrix-YouTube sharing.mov

This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.

From playlist Linear Algebra

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Column space of a matrix

We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the

From playlist Introducing linear algebra

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Definition of a matrix | Lecture 1 | Matrix Algebra for Engineers

What is a matrix? Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1

From playlist Matrix Algebra for Engineers

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Identity Matrix | Unit Matrix | Don't Memorise

This video explains the concept of an Identity Matrix. Is it also called a Unit Matrix? ✅To learn more about, Matrices, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=iks8wCfPerU&utm_term=%7Bkeyword%

From playlist Matrices

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Matrix Groups (Abstract Algebra)

Matrices are a great example of infinite, nonabelian groups. Here we introduce matrix groups with an emphasis on the general linear group and special linear group. The general linear group is written as GLn(F), where F is the field used for the matrix elements. The most common examples

From playlist Abstract Algebra

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Nijenhuis geometry for ECRs: Pre-recorded Lecture 2 Part A

Pre-recorded Lecture 2 Part A: Nijenhuis geometry for ECRs Date: 9 February 2022 Lecture slides: https://mathematical-research-institute.sydney.edu.au/wp-content/uploads/2022/02/Prerecorded_Lecture2.pdf ---------------------------------------------------------------------------------------

From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems

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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.)

From playlist Matrix Theory

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Example of Rational Canonical Form 3

Matrix Theory: We note two formulations of Rational Canonical Form. A recipe is given for combining and decomposing companion matrices using cyclic vectors.

From playlist Matrix Theory

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Singular Matrix and Non-Singular Matrix | Don't Memorise

This video explains what Singular Matrix and Non-Singular Matrix are! ✅To learn more about, Matrices, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=2OJJhfKwrRc&utm_term=%7Bkeyword%7D In this video,

From playlist Matrices

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Companion Matrices and Norms - Feb 10, 2021- Rings and Modules

This video is about companion matrices and norms. These are some tools that are useful when showing a quadratic integer ring is not a UFD (among other things).

From playlist Course on Rings and Modules (Abstract Algebra 4) [Graduate Course]

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Cayley-Hamilton Theorem: General Case

Matrix Theory: We state and prove the Cayley-Hamilton Theorem over a general field F. That is, we show each square matrix with entries in F satisfies its characteristic polynomial. We consider the special cases of diagonal and companion matrices before giving the proof.

From playlist Matrix Theory

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Two First Order Equations: Stability

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 View the complete course: http://ocw.mit.edu/RES-18-009F15 Instructor: Gilbert Strang A second order equation gives two first order equations. The matrix becomes a companion matrix (triang

From playlist MIT Learn Differential Equations

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Matrix Addition, Subtraction, and Scalar Multiplication

This video shows how to add, subtract and perform scalar multiplication with matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/

From playlist Introduction to Matrices and Matrix Operations

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Nijenhuis Geometry Chair's Talk 4 (Alexey Bolsinov)

SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Chair's Talk 4 (Alexey Bolsinov) 10 February 2022 ---------------------------------------------------------------------------------------------------------------------- SMRI-MATRIX Joint Symposium, 7 – 18 February 2022 Wee

From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems

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Eigenvalues and Stability: 2 by 2 Matrix, A

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 View the complete course: http://ocw.mit.edu/RES-18-009F15 Instructor: Gilbert Strang Two equations with a constant matrix are stable (solutions approach zero) when the trace is negative a

From playlist MIT Learn Differential Equations

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Elementary Matrices

This video defines elementary matrices and then provides several examples of determining if a given matrix is an elementary matrix. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Augmented Matrices

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Paola Boito: Topics in structured linear algebra - lecture 1

CIRM VIRTUAL EVENT Recorded during the meeting "French Computer Algebra Days" the March 01, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio

From playlist Virtual Conference

Related pages

Ferdinand Georg Frobenius | Frobenius normal form | Krylov subspace | Characteristic polynomial | Linear algebra | Frobenius endomorphism | Cyclic permutation | Minimal polynomial (linear algebra) | Vandermonde matrix | Cayley–Hamilton theorem | Circulant matrix | Monic polynomial | Recurrence relation | Cyclic module | Field (mathematics) | Square matrix | Basis (linear algebra) | Transpose | Generalizations of Pauli matrices