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- Equivalence theorem for nonsingular matrices: the matrix A is a change-of-basis matrix.#23670
- Equivalence theorem for nonsingular matrices: the matrix A represents the identity map with respect to some pair of bases.#23671
- Equivalence theorem for nonsingular matrices: the matrix A row-reduces to the identity matrix.#23656
- Equivalence theorem for nonsingular matrices: the nullity of the matrix A is 0.#23668
- Equivalence theorem for nonsingular matrices: the null space of the matrix A is {0}.#23667
- Equivalence theorem for nonsingular matrices: there is a pivot position in every row of A.#23655
- Equivalence theorem for nonsingular matrices: the rows of A are a basis for R^n (or C^n).#23652
- Equivalence theorem for nonsingular matrices: the rows of A are linearly independent.#23650
- Equivalence theorem for nonsingular matrices: the rows of A span R^n (or C^n).#23648
- Equivalence theorem for nonsingular matrices: the transpose of the matrix A has an inverse.#23660
- Equivalence theorems for injective transformations#24077
- Equivalent matrices represent the same linear transformation with resect to appropriate bases.#23605
- Every basis for a vector space contains the same number of elements#24008
- Every finite dimensional vector space over R (or C) is isomorphic to R^n (or C^n) for some n.#24006
- Every matrix has an eigenvalue over the complex numbers.#23687
- Every matrix is row-equivalent to a matrix in reduced row echelon form.#23548
- Every matrix is row-equivalent to only one matrix in reduced row echelon form.#23549
- Every nilpotent matrix is similar to one with 1 on subdiagonal blocks and all other entries 0.#23582
- Every square matrix is conjugate#23566
- Every square matrix is similar the sum of a diagonal and a nilpotent matrix.#23585
- Every square matrix is similar to one in Jordan form.#23639
- Example of a linear transformation on R^2: generic#23888
- Example of a linear transformation on R^2: projection#23891
- Example of a linear transformation on R^2: rotation#23890
- Example of a linear transformation on R^2: shear#23889
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