GraphMath

Inverse

Undoing a transformation — intuition, definition and computation.

This chapter presents the inverse matrix: what it means, when it exists, why it is unique, and how it is used in solving A x = b.

Chapter contents

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Topic Pages
Algebraic & geometric definition 1
Computing M⁻¹ by row reduction of [ M | I ] 2
Uniqueness of M⁻¹ 3
M⁻¹ is defined only for square full-rank M 4
Algebraic properties of M⁻¹ 5–6
Visual example of (AB)⁻¹ 7
M⁻¹ as solution to A×x⃗ = b⃗ 8
Trivial cases: 1×1 and 2×2 9–10

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