University Linear Algebra Vector Spaces and Subspaces — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 5 definitions and 6 theorems, 6 worked examples, 2 diagrams, in 12 printable pages. This page lists what the notes cover. The notes themselves come with the University Linear Algebra bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Vector Spaces and Subspaces — what the notes cover
7 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Vectors in n-space and linear combinations
- Definition — Vectors in n-space
- Definition — Linear combination
- Theorem — A linear system as a vector equation
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
The vector space axioms
- Definition — Vector space
Also in this section: 1 worked example, 1 note on method and common errors.
Consequences of the axioms
- Theorem — Basic consequences of the axioms
Also in this section: 1 worked example, 1 note on method and common errors.
Spaces of polynomials, matrices and functions
- Definition — The standard vector spaces
- Theorem — Equality of vectors in these spaces
Also in this section: 1 worked example, 1 note on method and common errors.
The subspace test
- Definition — Subspace
- Theorem — The subspace test
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Solution sets of homogeneous systems
- Theorem — The solution set of a homogeneous system
- Theorem — Solutions of a non-homogeneous system
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Linear Algebra Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Vector Spaces and Subspaces practice worksheet is free and stays free.
Every University Linear Algebra topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Linear Algebra units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Vector Spaces and Subspaces practice worksheet About the Vector Spaces and Subspaces unit test