Determinant

Definition, properties and computation

This chapter defines the determinant, derives its main properties, explains computation by row reduction, and includes the transpose, orthonormal, permutation and cofactor viewpoints.

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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
\| A B \| = \| A \|×\| B \|	6–7
Determinant of a triangular matrix and determinant computation	7–9
Determinant of M transposed	9–10
Determinant of orthonormal matrix	11–12
Illustration of permutation method	12–14
Illustration of cofactor expansion method	14–17
Summary	17–18

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