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Introduction to algebra
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I · Algebra basics
Chapter I.3
Determinants
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I.3.1 · Determinants: construction and basic properties
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I.3.2 · Further properties of determinants
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I.3.3 · Applications of determinants
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I.3.4 · Towards the construction of the theory of determinants
Section I.3.1
Determinants: construction and basic properties
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Subsection I.3.1.1
Geometric motivation
Subsection I.3.1.2
Combinatorial-analytic approach
Subsection I.3.1.3
Main properties of determinants
Section I.3.2
Further properties of determinants
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Subsection I.3.2.1
Expansion of the determinant by the elements of a column or row
Subsection I.3.2.2
Determinants of special matrices
Section I.3.3
Applications of determinants
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Subsection I.3.3.1
The criterion for non-degeneracy of a matrix
Subsection I.3.3.2
Cramer's formulas
Subsection I.3.3.3
The method of bordering minors
Section I.3.4
Towards the construction of the theory of determinants
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Subsection I.3.4.1
The first axiomatic construction
Subsection I.3.4.2
The second axiomatic construction
Subsection I.3.4.3
Construction by the method of complete induction
Subsection I.3.4.4
Characterization by multiplicative properties