Note collections

MATH1030: Linear algebra I

Rigorous linear algebra notes on systems, matrices, structure, and proof, with interaction used only where it clarifies the mathematics.

Language

EN 繁简

All note collections Series overview

Chapter 1

Systems of equations

Learn to read equations as full solution sets.

1.1

1.1 Equations and solution sets

Chapter 2

Matrices and elimination

Build matrix intuition and use row reduction with purpose.

2.1

2.1 Matrix basics

2.2

2.2 Augmented matrices and row operations

2.3

2.3 Gaussian elimination and RREF

2.4

2.4 Solution-set types

Chapter 3

Matrix algebra

Matrix multiplication, transpose, and structural matrix notation.

3.1

3.1 Matrix multiplication and identity matrices

3.2

3.2 Transpose and special matrices

Chapter 4

Solution structure

Homogeneous systems, null spaces, and the shape of full solution sets.

4.1

4.1 Homogeneous systems and null space

Chapter 5

Invertibility

Understand when a matrix can be undone and why that matters.

5.1

5.1 Invertible matrices

Member

Chapter 6

Vector spaces

Move from matrix procedures to the structure of spaces, span, independence, and basis.

6.1

6.1 Vector spaces

Member

6.2

6.2 Subspaces

Member

6.3

6.3 Linear combinations and span

Member

6.4

6.4 Linear dependence and independence

Member

6.5

6.5 Basis and dimension

Member

6.6

6.6 Column space, row space, and rank

Member

Chapter 7

Determinants

Determinants, cofactor formulas, and the structural algebra that connects row operations, transpose, and invertibility.

7.1

7.1 Determinants and cofactor expansion

Member

7.2

7.2 Row operations, products, and invertibility

Member

7.3

7.3 Transpose, column operations, and Cramer's rule

Member

Chapter 8

Eigenvalues and diagonalization

Eigenvalues, eigenspaces, similarity, and diagonalization as the next structural layer after determinants.

8.1

8.1 Eigenvalues, eigenvectors, and eigenspaces

Member

8.2

8.2 Diagonalization and similarity

Member

8.3

8.3 Characteristic polynomials and diagonalization tests

Member

Chapter 9

Inner products and orthogonality

Inner products, orthogonality, orthonormal bases, and Gram-Schmidt as the geometric layer after eigenvalues.

9.1

9.1 Inner products, norms, and angles

Member

9.2

9.2 Orthogonal sets and orthonormal bases

Member

9.3

9.3 Gram-Schmidt orthogonalization

Member

9.4

9.4 Cauchy-Schwarz and triangle inequalities

Member

7.2Source-backedMemberEstimated reading time: 10 min

7.2 Row operations, products, and invertibility

Track exactly how row operations change determinants, then connect that behavior to multiplicativity, inverse matrices, and invertibility tests.

Note collections

MATH1030: Linear algebra I

Rigorous linear algebra notes on systems, matrices, structure, and proof, with interaction used only where it clarifies the mathematics.

Language

EN 繁简

All note collections Series overview

Chapter 1

Systems of equations

Learn to read equations as full solution sets.

1.1

1.1 Equations and solution sets

Chapter 2

Matrices and elimination

Build matrix intuition and use row reduction with purpose.

2.1

2.1 Matrix basics

2.2

2.2 Augmented matrices and row operations

2.3

2.3 Gaussian elimination and RREF

2.4

2.4 Solution-set types

Chapter 3

Matrix algebra

Matrix multiplication, transpose, and structural matrix notation.

3.1

3.1 Matrix multiplication and identity matrices

3.2

3.2 Transpose and special matrices

Chapter 4

Solution structure

Homogeneous systems, null spaces, and the shape of full solution sets.

4.1

4.1 Homogeneous systems and null space

Chapter 5

Invertibility

Understand when a matrix can be undone and why that matters.

5.1

5.1 Invertible matrices

Member

Chapter 6

Vector spaces

Move from matrix procedures to the structure of spaces, span, independence, and basis.

6.1

6.1 Vector spaces

Member

6.2

6.2 Subspaces

Member

6.3

6.3 Linear combinations and span

Member

6.4

6.4 Linear dependence and independence

Member

6.5

6.5 Basis and dimension

Member

6.6

6.6 Column space, row space, and rank

Member

Chapter 7

Determinants

Determinants, cofactor formulas, and the structural algebra that connects row operations, transpose, and invertibility.

7.1

7.1 Determinants and cofactor expansion

Member

7.2

7.2 Row operations, products, and invertibility

Member

7.3

7.3 Transpose, column operations, and Cramer's rule

Member

Chapter 8

Eigenvalues and diagonalization

Eigenvalues, eigenspaces, similarity, and diagonalization as the next structural layer after determinants.

8.1

8.1 Eigenvalues, eigenvectors, and eigenspaces

Member

8.2

8.2 Diagonalization and similarity

Member

8.3

8.3 Characteristic polynomials and diagonalization tests

Member

Chapter 9

Inner products and orthogonality

Inner products, orthogonality, orthonormal bases, and Gram-Schmidt as the geometric layer after eigenvalues.

9.1

9.1 Inner products, norms, and angles

Member

9.2

9.2 Orthogonal sets and orthonormal bases

Member

9.3

9.3 Gram-Schmidt orthogonalization

Member

9.4

9.4 Cauchy-Schwarz and triangle inequalities

Member

This advanced section is available to members.

Upgrade membership

Prerequisites

7.1

7.1 Determinants and cofactor expansion

5.1

5.1 Invertible matrices

Key terms in this unit

More notes in this series

Previous section

7.1 Determinants and cofactor expansion

Next section

7.3 Transpose, column operations, and Cramer's rule