MathLiveEigendecomposition of a matrix
Writes a diagonalizable square matrix as a product of a matrix of its eigenvectors, a diagonal matrix of its eigenvalues, and the inverse of the eigenvector matrix. It is used to simplify matrix powers, functions of matrices, and solving linear systems of differential equations.
A = V\Lambda V^{-1}What the symbols mean
| the diagonalizable square matrix being decomposed | |
| matrix whose columns are the eigenvectors of A | |
| diagonal matrix whose diagonal entries are the eigenvalues of A | |
| inverse of the eigenvector matrix V |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledeigenvalue decomposition, eigen decomposition, diagonalization of a matrix, matrix diagonalization
- SourceWikidata Q194919
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