Numerical linear algebra | Matrices

Diagonally dominant matrix

In mathematics, a square matrix is said to be diagonally dominant if, for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row. More precisely, the matrix A is diagonally dominant if where aij denotes the entry in the ith row and jth column. Note that this definition uses a weak inequality, and is therefore sometimes called weak diagonal dominance. If a strict inequality (>) is used, this is called strict diagonal dominance. The unqualified term diagonal dominance can mean both strict and weak diagonal dominance, depending on the context. (Wikipedia).

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The Diagonalization of Matrices

This video explains the process of diagonalization of a matrix.

From playlist The Diagonalization of Matrices

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Diagonal Matrices

This video defines a diagonal matrix and then explains how to determine the inverse of a diagonal matrix (if possible) and how to raise a diagonal matrix to a power. Site: mathispower4u.com Blog: mathispower4u.wordpress.com

From playlist Introduction to Matrices and Matrix Operations

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Block Diagonal Matrices

Every operator on a finite-dimensional complex vector space has a matrix (with respect to some basis of the vector space) that is a block diagonal matrix, with each block itself an upper-triangular matrix that contains only one eigenvalue on the diagonal.

From playlist Linear Algebra Done Right

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From playlist Diagonalization

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From playlist Symmetric Matrices

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In this lecture, we discuss what it means for a square matrix to be diagonalizable. We prove the Diagonalization Theorem, which tells us exactly when a matrix is diagonalizable.

From playlist Linear Algebra Lectures

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Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ Many, MANY thanks to Dean @deanencoded for designing my openin

From playlist AQA A-Level Further Maths C11: Diagonalisation

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From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University

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From playlist Numerical Computation spring 2015. Wen Shen. Penn State University.

Related pages

Gershgorin circle theorem | Weakly chained diagonally dominant matrix | Gauss–Seidel method | Finite element method | Pivot element | Temperley–Lieb algebra | Jacobi method | Gaussian elimination | Matrix (mathematics) | Hermitian matrix