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- A set of vectors is linearly independent if and only if the matrix of column vectors in reduced row-echelon form has every column as a pivot column.#23824
- A subset of a linearly independent set is linearly independent.#23980
- A vector can be written uniquely as a linear combination of vectors from independent subspaces.#23973
- A vector can be written uniquely as a sum of a vector in a subspace and a vector orthogonal to the subspace.#23934
- A vector is in the orthogonal complement of a subspace if and only if it is orthogonal to every vector in a basis of the subspace.#23923
- Axioms of a vector space#23798
- Bases#23828
- Basic properties#23957
- Basic properties of linear transformations#23863
- Basic terminology#23412
- Basic terminology and notation#23448
- Block matrices#23567
- Canonical forms of matrices#23608
- Change of coordinates matrices are invertible#23998
- Characteristic and minimal polynomials#23699
- C^n is a vector space.#24098
- Cofactors#23716
- Composition#24022
- Conjugating by a change of coordinates matrix converts matrix representations with respect to different bases.#23999
- Conjugation#23464
- Container for Linear Algebra#24123
- Coordinates#23989
- Coordinate vector spaces#23776
- Cramer's rule#23722
- Definition and terminology#23954