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- The solutions to a homogeneous linear differential equation is a vector space.#24102
- The solutions to a homogeneous system of linear equations is a vector space.#24101
- The solutions to a nonhomogeneous system are given by a particular solution plus the solutions to the homogeneous system.#23445
- The span of a set of vectors is a subspace#23977
- The spectral theorem for symmetric matrices#23575
- The standard inner product of a vector with itself is 0 only for the 0 vector#23903
- The standard inner product of a vector with itself is non-negative#23902
- The standard inner product on C^n can be written as the product of a vector and the adjoint of a vector.#23905
- The standard inner product on C^n commutes/anticommutes with scalar multiplication.#23900
- The standard inner product on C^n is anticommutative.#23898
- The standard inner product on R^n can be written as the product of a vector and the transpose of a vector.#23904
- The standard inner product on R^n commutes with (real) scalar multiplication.#23899
- The standard inner product on R^n is commutative.#23897
- The standard inner product on R^n (or C^n) distributes over addition.#23901
- The standard/natural basis of R^n (or C^n) is a basis.#23831
- The sum of linear transformations is a linear transformation#24016
- The sum of subspaces is a subspace#23969
- The the image of a spanning set is a spanning set for the range space#24037
- The transpose of a product of matrices is the product of the transposes in reverse order.#23512
- The transpose of a sum of matrices is the sum of the transposes.#23510
- The triangle inequality#23912
- The union of bases from independent subspaces is a basis for the space.#23974
- TODO: Linear Algebra Content Progress#29496
- Transpose and adjoint#23502
- Transpose commutes with scalar multiplication.#23511
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