Navigate
Jump to a node in this tree, or explore your trees and public knowledge.
Quick Navigation
Jump to a node or explore another tree.
26–50 of 718 nodes
- A linear transformation is surjective if and only if the image of a basis is a spanning set#24038
- A linear transformation is surjective if and only if the rank equals the dimension of the codomain.#24035
- A linear transformation maps 0 to 0.#23864
- A linear transformation of a linear combination is the linear combination of the linear transformation#23865
- All echelon forms of a linear system have the same free variables#23423
- A matrix and its transpose have the same determinant.#23728
- A matrix and its transpose have the same eigenvalues/characteristic polynomial.#23693
- A matrix equation is equivalent to a linear system#23767
- A matrix is orthogonally diagonalizable if and only if it is symmetric.#23578
- A matrix of rank k is equivalent to a matrix with 1 in the first k diagonal entries and 0 elsewhere.#23606
- A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.#23906
- A matrix with a 0 row/column has determinant 0#23741
- A matrix with real entries and orthonormal columns preserves dot products.#23932
- A matrix with real entries and orthonormal columns preserves norms.#23931
- A matrix with real entries has eigenvalues occurring in conjugate pairs.#23710
- A matrix with two equal rows/columns has determinant 0#23740
- An eigenspace of a matrix is a nontrivial subspace.#23685
- An eigenspace of a matrix is the null space of a related matrix.#23686
- An n-by-n complex matrix has n eigenvalues counting multiplicity#23698
- An n-by-n matrix is diagonalizable if and only if it has n linearly independent eigenvectors.#23612
- An n-by-n matrix is diagonalizable if and only if the sum of the dimensions of the eigenspaces equals n.#23613
- An n-by-n matrix is diagonalizable if and only if the union of the basis vectors for the eigenspaces is a basis for R^n (or C^n).#23616
- An n-by-n matrix with n distinct eigenvalues is diagonalizable.#23617
- A nonempty subset of a vector space is a subspace if and only if it is closed under linear combinations#23965
- A nonsingular matrix can be written as a product of elementary matrices.#23558