inverse matrix

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 ${\displaystyle V^{*}}$? Fill the columns of a square matrix M with the basis vectors of V. Find the inverse matrix ${\displaystyle M^{-1}}$ of M. Then the rows of ${\displaystyle M^{-1}}$ are the (co)vectors of that dual basis. Since ${\displaystyle (M^{-1})^{-1}=M}$, then ${\displaystyle (V^{*})^{*}=V}$.

• inverse