Eigenvectors — Topic Summaries
AI-powered summaries of 9 videos about Eigenvectors.
9 summaries
Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
Eigenvectors are the vectors that stay on their own span under a linear transformation—meaning the transformation only stretches or squishes them,...
Linear Algebra 54 | Characteristic Polynomial
Eigenvalues can be found by turning a matrix problem into a single-variable polynomial: the characteristic polynomial. For a square matrix A, an...
Linear Algebra 53 | Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors identify the special directions a linear transformation preserves—up to scaling—when a matrix acts on space. For a...
Linear Algebra 57 | Spectrum of Triangular Matrices
Eigenvalues of triangular and certain block matrices can be read off directly—often without computing determinants or solving characteristic...
Linear Algebra 53 | Eigenvalues and Eigenvectors [dark version]
Eigenvalues and eigenvectors identify directions that a linear transformation preserves up to scaling—turning a complicated matrix action into a...
Linear Algebra 54 | Characteristic Polynomial [dark version]
Eigenvalues can be found by turning a matrix problem into a single polynomial equation: for a square matrix A, the eigenvalues are exactly the zeros...
Ordinary Differential Equations 23 | Example for Matrix Exponential
A 2×2 homogeneous, autonomous linear system can be solved cleanly by converting it into a matrix exponential—then making that exponential computable...
Linear Algebra 65 | Diagonalizable Matrices [dark version]
Diagonalizable matrices are exactly the square matrices that admit a full set of eigenvectors—enough to rebuild every vector in the space—so the...
Abstract Linear Algebra 34 | Eigenvalues and Eigenvectors for Linear Maps
Eigenvectors and eigenvalues for a linear map are defined by a simple “scaling” condition: a nonzero vector X is an eigenvector of L if L(X) lands in...