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Examples of vector spaces

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The solutions to a homogeneous linear differential equation is a vector space.
The set of all polynomials is a vector space.
The set of all polynomials of degree at most n is a vector space.
The set of all sequences is a vector space.
The crazy vector space is a vector space.
The set containing only 0 is a vector space.
F^n is a vector space.
R^n is a vector space.
C^n is a vector space.
The set of all functions on a set is a vector space.
The solutions to a homogeneous system of linear equations is a vector space.
The set of m by n matrices is a vector space.
The row space of a matrix is a vector space
The column space of a matrix is a vector space
The null space of a matrix is a subspace of R^n (or C^n).
The left null space of a matrix is a subspace of R^m (or C^m).
The set of linear transformations between two vector spaces is a vector space.

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The null space of a matrix is a subspace of R^n (or C^n).

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Definition of matrix null space (right)Close match
The left null space of a matrix is a subspace of R^m (or C^m).Close match
Equivalence theorem for nonsingular matrices: the null space of the matrix A is {0}.Close match
Definition of nullity of a matrixClose match
Definition of matrix null space (left)Close match
Rank–nullity theorem for an m-by-n matrixClose match
Subspaces associated to a matrixClose match
The row space of a matrix is a vector spaceClose match
The set of m by n matrices is a vector space.Close match
The solutions to a homogeneous system of linear equations is a vector space.Close match
Null spaces are orthogonal complements of the corresponding row or column spacesClose match
Rank and nullityClose match
Equivalence theorem for nonsingular matrices: the nullity of the matrix A is 0.Close match
The column space of a matrix is a vector spaceClose match
Definition of 0 matrixClose match
The column space of an m-by-n matrix is a subspace of R^m (or C^m)Close match
Equivalence theorem for nonsingular matrices: the columns of A span R^n (or C^n).Close match
Equivalence theorem for nonsingular matrices: the rows of A span R^n (or C^n).Close match
R^n is a vector space.Close match
Equivalence theorem for nonsingular matrices: the dimension of the column space of A is n.Close match

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