inverse matrix

English

inverse matrix (plural inverse matrices or inverse matrixes)

(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 ${\\displaystyle (V^{*})^{*}=V}$ .

linear algebra