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Course contents

Linear algebra I

All note collections Series overview

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35 sections

1.1 Equations and solution sets 1.2 Reading theorems and proof language

2.1 Matrix basics 2.2 Augmented matrices and row operations 2.3 Gaussian elimination and RREF 2.4 Solution-set types 2.5 Existence of row-echelon forms

3.1 Matrix addition, subtraction, and scalar multiplication 3.2 Matrix multiplication, identity matrices, and linear systems 3.3 Transpose, symmetric, and skew-symmetric matrices 3.4 Special matrices 3.5 Elementary row-operation matrices 3.6 Block matrices

4.1 Homogeneous systems and null space 4.2 Set language and solution sets

5.1 Invertible matricesMembership required 5.2 RREF uniqueness and well-defined rankMembership required

6.1 Vector spacesMembership required 6.2 SubspacesMembership required 6.3 Linear combinations and spanCurrent sectionMembership required 6.4 Linear dependence and independenceMembership required 6.5 Basis and dimensionMembership required 6.6 Column space, row space, and rankMembership required 6.7 Matrix subspaces, basis, and dimensionMembership required 6.8 Basis extension and change of basisMembership required

7.1 Determinants and cofactor expansionMembership required 7.2 Row operations, products, and invertibilityMembership required 7.3 Transpose, column operations, and Cramer's ruleMembership required

8.1 Eigenvalues, eigenvectors, and eigenspacesMembership required 8.2 Diagonalization and similarityMembership required 8.3 Characteristic polynomials and diagonalization testsMembership required

9.1 Inner products, norms, and anglesMembership required 9.2 Orthogonal sets and orthonormal basesMembership required 9.3 Gram-Schmidt orthogonalizationMembership required 9.4 Cauchy-Schwarz and triangle inequalitiesMembership required

Notes Linear algebra IVector spaces

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6.3Member

6.3 Linear combinations and span

Treat linear combinations as controlled building instructions, then see span as every vector you can build that way.

Course contents

Linear algebra I

All note collections Series overview

Search notes in this course

35 sections

1.1 Equations and solution sets 1.2 Reading theorems and proof language

2.1 Matrix basics 2.2 Augmented matrices and row operations 2.3 Gaussian elimination and RREF 2.4 Solution-set types 2.5 Existence of row-echelon forms

4.1 Homogeneous systems and null space 4.2 Set language and solution sets

5.1 Invertible matricesMembership required 5.2 RREF uniqueness and well-defined rankMembership required

7.1 Determinants and cofactor expansionMembership required 7.2 Row operations, products, and invertibilityMembership required 7.3 Transpose, column operations, and Cramer's ruleMembership required

8.1 Eigenvalues, eigenvectors, and eigenspacesMembership required 8.2 Diagonalization and similarityMembership required 8.3 Characteristic polynomials and diagonalization testsMembership required

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Series overview

Prerequisites

6.1

6.1 Vector spaces

Key terms in this unit

More notes in this series

Previous section

6.2 Subspaces

Next section

6.4 Linear dependence and independence