Matrix inverse
An inverse reverses a square linear transformation. A square matrix is invertible exactly when it has full rank.
Definition
An inverse reverses a square linear transformation. A square matrix is invertible exactly when it has full rank.
Intuition
A map that collapses different inputs onto one output cannot be uniquely undone.
Worked example
The diagonal matrix diag(2, 4) has inverse diag(1/2, 1/4).
The math
For an invertible square matrix, .
In machine learning
Use invertibility to reason about uniqueness; for numerical solutions prefer solving Ax = b directly.
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Sources
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