Invertible Linear Map

An invertible linear transformation T:V->W is a map between vector spaces V and W with an inverse map which is also a linear transformation. When T is given by matrix multiplication, i.e., T(v)=Av, then T is invertible iff A is a nonsingular matrix. Note that the dimensions of V and W must be the same.

See also

Linear Transformation, Matrix, Nonsingular Matrix, Vector Space

This entry contributed by Todd Rowland

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Rowland, Todd. "Invertible Linear Map." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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