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 Space
*This entry contributed by Todd
Rowland*

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## Cite this as:

Rowland, Todd. "Invertible Linear Map." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/InvertibleLinearMap.html