91影视

Two vector spaces V and W over the same field F are isomorphic if there is a bisection$\mathit{T}\mathbf{:}\mathit{V}\mathbf{鈫�}\mathit{W}$which preserves addition and scalar multiplication, that is, for all vectors u and v in V, and all scalars $\mathbf{c}\mathbf{鈭�}\mathbf{F}\mathbf{,}\mathbf{T}\mathbf{(}\mathbf{u}\mathbf{+}\mathbf{v}\mathbf{)}\mathbf{=}\mathbf{T}\mathbf{\left(}\mathbf{u}\mathbf{\right)}\mathbf{+}\mathbf{T}\mathbf{\left(}\mathbf{v}\mathbf{\right)}$and. The correspondence T is called an isomorphism of vector spaces.

When $T:V鈫�W$is an isomorphism, then $T:V^{\text{'}}鈫�W$it emphasize that it is an isomorphism When V and W, are isomorphic, but the specific isomorphism is not named, we鈥檒l just write $V~=W$.

The matrix of linear transformation T is regular (its determinant is -1), so T has nullity 0.

Also, from the form of a matrix, it concludes that T is a transformation from two-dimensional to two-dimensional space.

Since nullity is 0, the rank must be 2.

Hence, the statement is true.