Let K {\displaystyle {}K} denote a field and let V {\displaystyle {}V} and W {\displaystyle {}W} denote finite-dimensional K {\displaystyle {}K} -vector spaces. Let v = v 1 , … , v n {\displaystyle {}{\mathfrak {v}}=v_{1},\ldots ,v_{n}} be a basis of V {\displaystyle {}V} and w = w 1 , … , w m {\displaystyle {}{\mathfrak {w}}=w_{1},\ldots ,w_{m}} be a basis of W {\displaystyle {}W} .
is an isomorphism