Determinant

Signed volume scaling and practical computation

This chapter defines the determinant by how it changes under elementary row operations, connects it to signed volume scaling and shows how to compute it efficiently via row reduction.

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Chapter contents

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Topic	Pages
Definition	1–3
Determinant of elementary matrices	4
Determinant of non-full-rank M	5
\| AB \| = \| A \| × \| B \|	6–7
Determinant of a triangular matrix and determinant computation	8–9
Determinant of M transposed	10
Determinant of orthonormal matrix	11
Illustration of permutation method	12–14
Illustration of cofactor expansion method	15–17
Summary	18

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