inverse matrix

English

Noun

inverse matrix (plural inverse matrices or inverse matrixes)

1. (linear algebra) Of a matrix A, another matrix B such that A multiplied by B and B multiplied by A both equal the identity matrix.

   Given the basis of some vector space V, how to find its dual basis, i.e., the basis of the dual space $V^{*}$? Fill the columns of a square matrix M with the basis vectors of V. Find the inverse matrix $M^{-1}$ of M. Then the rows of $M^{-1}$ are the (co)vectors of that dual basis. Since $(M^{-1})^{-1}=M$, then $(V^{*})^{*}=V$.

Synonyms

• inverse

Translations

linear algebra

• Estonian: pöördmaatriks
• Finnish: käänteismatriisi (fi)
• French: matrice inverse (fr) f
• German: inverse Matrix f, Inverse f, Kehrmatrix f
• Japanese: 逆行列 (ja) (gyaku-gyōretsu)
• Russian: обра́тная ма́трица f (obrátnaja mátrica)
• Spanish: matriz inversa f
• Swedish: invers matris c