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).
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
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
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
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
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
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
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
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
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
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
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]
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
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
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
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
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
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
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