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

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Chapter 6

Vector spaces

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

6.1

6.1 Vector spaces

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6.2

6.2 Subspaces

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6.3

6.3 Linear combinations and span

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6.4

6.4 Linear dependence and independence

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6.5

6.5 Basis and dimension

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6.6

6.6 Column space, row space, and rank

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6.3Source-backedEmbedded interactionMemberEstimated reading time: 2 min

6.3 Linear combinations and span

Treat span as a precise set of outputs, connect it to linear systems, and learn how to decide whether a vector can or cannot be built from a given list.

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

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6.5

6.5 Basis and dimension

Member

6.6

6.6 Column space, row space, and rank

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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