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- Abstract vector spaces#23953
- A consistent system with more variables than equations has infinitely many solutions.#23440
- Adding a multiple of one row to another row does not change the determinant.#23737
- Addition#23461
- A determinant is a multilinear function#23736
- A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns.#23615
- Adjoining an element not in the span of a linearly independent set gives another linearly independent set.#23983
- A homogeneous system has a nontrivial solution if and only if it has a free variable.#23437
- A homogeneous system with more variables than equations has infinitely many solutions.#23441
- Algebraic properties of R^n (or C^n)#23777
- Algorithm for computing an LU decomposition#23626
- A linear system is equivalent to a matrix equation.#23753
- A linear system is equivalent to a vector equation.#23752
- A linear transformation has a representation as an upper triangular matrix.#24076
- A linear transformation has the same eigenvalues and eigenvectors as any matrix representation.#24075
- A linear transformation is determined by its action on a basis.#23866
- A linear transformation is diagonalizable if there is a basis such that each element is an eigenvector of the transformation.#24054
- A linear transformation is given by a matrix whose columns are the images of the standard basis vectors#23858
- A linear transformation is given by a matrix with respect to a given basis.#23859
- A linear transformation is given by multiplying by its matrix representation with respect to bases of the spaces#24069
- A linear transformation is injective on its generalized range space.#24040
- A linear transformation is invertible if and only if it is injective and surjective#24067
- A linear transformation is onto if and only if its rank equals the number of rows in any matrix representation.#24066
- A linear transformation is surjective if and only if the columns of its matrix span the codomain.#23885
- A linear transformation is surjective if and only if the image of a basis is a spanning set#24038
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