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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.
A subset of a linearly independent set is linearly independent.
A vector can be written uniquely as a linear combination of vectors from independent subspaces.
A vector can be written uniquely as a sum of a vector in a subspace and a vector orthogonal to the subspace.
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.
Axioms of a vector space
Bases
Basic properties
Basic properties of linear transformations
Basic terminology
Basic terminology and notation
Block matrices
Canonical forms of matrices
Change of coordinates matrices are invertible
Characteristic and minimal polynomials
C^n is a vector space.
Cofactors
Composition
Conjugating by a change of coordinates matrix converts matrix representations with respect to different bases.
Conjugation
Container for Linear Algebra
Coordinates
Coordinate vector spaces
Cramer's rule
Definition and terminology

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