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Introduction to algebra
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I · Algebra basics
Chapter I.2
Matrices
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I.2.1 · Row and column vector spaces
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I.2.2 · Matrix rank
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I.2.3 · Linear mappings. Operations with matrices
Section I.2.1
Row and column vector spaces
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Subsection I.2.1.1
Motivation
Subsection I.2.1.2
Main definitions
Subsection I.2.1.3
Linear combinations. Linear span
Subsection I.2.1.4
Linear dependence
Subsection I.2.1.5
Basis. Dimension
Section I.2.2
Matrix rank
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Subsection I.2.2.1
Return to the equations
Subsection I.2.2.2
Matrix rank
Subsection I.2.2.3
Consistency criterion
Section I.2.3
Linear mappings. Operations with matrices
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Subsection I.2.3.1
Matrices and mappings
Subsection I.2.3.2
Matrix multiplication
Subsection I.2.3.3
Matrix transposition
Subsection I.2.3.4
Rank of the product of matrices
Subsection I.2.3.5
Square matrices
Subsection I.2.3.6
Equivalence classes of matrices
Subsection I.2.3.7
Computing the inverse matrix
Subsection I.2.3.8
Solution space