MathLiveInverse matrix definition
A square matrix A has an inverse A^{-1} exactly when its determinant is nonzero, and multiplying A by its inverse on either side gives the identity matrix. It is used to define and test invertibility in linear algebra.
\boldsymbol{A}\boldsymbol{A}^{-1}=\boldsymbol{A}^{-1}\boldsymbol{A}=\boldsymbol{I},\quad \det \boldsymbol{A}\neq 0What the symbols mean
| square matrix | |
| inverse of the matrix \boldsymbol{A} | |
| identity matrix of the same size as \boldsymbol{A} | |
| determinant of \boldsymbol{A} |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledmatrix inverse, inverse of a square matrix, inverse of a matrix, A times A inverse equals identity, invertible matrix condition, matrix inverse determinant nonzero
- SourceWikidata Q17123743
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