The solutions to a nonhomogeneous system are given by a particular solution plus the solutions to the homogeneous system.
The span of a set of vectors is a subspace
The spectral theorem for symmetric matrices
The standard inner product of a vector with itself is 0 only for the 0 vector
The standard inner product of a vector with itself is non-negative
The standard inner product on C^n can be written as the product of a vector and the adjoint of a vector.
The standard inner product on C^n commutes/anticommutes with scalar multiplication.
The standard inner product on C^n is anticommutative.
The standard inner product on R^n can be written as the product of a vector and the transpose of a vector.
The standard inner product on R^n commutes with (real) scalar multiplication.
The standard inner product on R^n is commutative.
The standard inner product on R^n (or C^n) distributes over addition.
The standard/natural basis of R^n (or C^n) is a basis.
The sum of linear transformations is a linear transformation
The sum of subspaces is a subspace
The the image of a spanning set is a spanning set for the range space
The transpose of a product of matrices is the product of the transposes in reverse order.
The transpose of a sum of matrices is the sum of the transposes.
The triangle inequality
The union of bases from independent subspaces is a basis for the space.
TODO: Linear Algebra Content Progress
Transpose and adjoint
Transpose commutes with scalar multiplication.
Triangular matrices
Two matrices of the same size are equivalent if and only if they have the same rank.

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