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