Basis matrix
= Basis matrix
{title2=$B=[b_1\ \cdots\ b_n]$}
A <matrix> whose columns are the <coordinate vectors> of an ordered <basis> in a fixed reference <basis>. It is an <invertible matrix>, and multiplication by it converts <coordinates> in the column <basis> to the reference <coordinates>: $v=B[v]_B$. For a real <inner product space> with orthonormal reference <basis>, its <Gram matrix> is $B^TB$, and its <reciprocal basis> has <basis matrix> $B^{-T}$.