An invertible linear transformation is a map between vector spaces and with an inverse map which is also a linear transformation. When is given by matrix multiplication, i.e., , then is invertible iff is a nonsingular matrix. Note that the dimensions of and must be the same.
Invertible Linear Map
See also
Linear Transformation, Matrix, Nonsingular Matrix, Vector SpaceThis 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. https://mathworld.wolfram.com/InvertibleLinearMap.html