Description of a spanning set for the null space of a matrix from the reduced row-echelon form.
Description of the Gram-Schmidt process
Determinants
Determinants and operations on matrices
Determinants axiomatically
Determine if a particular set of vectors in R^3 in linearly independent
Determine if a particular set of vectors spans R^3
Determine if a particular vector is in the span of a set of vectors
Determine if a particular vector is in the span of a set of vectors in R^2
Determine if a particular vector is in the span of a set of vectors in R^3
Dimension
Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.
Each vector can be written uniquely as a linear combination of vectors from a given basis.
Echelon matrices
Eigenspaces
Eigenvalues and eigenvectors
Eigenvalues and operations on matrices
Eigenvectors of a symmetric matrix with different eigenvalues are orthogonal.
Eigenvectors with distinct eigenvalues are linearly independent.
Elementary matrices
Elementary matrices are invertible/nonsingular.
Equation operations on a linear system give an equivalent system.
Equivalence theorem for injective linear transformations: The columns of the matrix of T are linearly independent.
Equivalence theorem for injective linear transformations: The image of a basis for V is a basis for the range of T.
Equivalence theorem for injective linear transformations: The inverse of T is a linear transformation on its range.

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