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  • Multiplication

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  • Definition of matrix multiplication in terms of column vectors
  • Definition of matrix multiplication
  • Theorem describing matrix multiplication
  • Any matrix times the 0 matrix equals the 0 matrix.
  • Example of multiplying 2x2 matrices
  • Example of multiplying 3x3 matrices
  • Example of multiplying nonsquare matrices
  • Example of multiplying matrices
  • Matrix multiplication is associative.
  • Matrix multiplication is distributive over matrix addition.
  • The identity matrix is the identity for matrix multiplication.
  • Matrix multiplication is not commutative in general.
  • For matrices
  • Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectors
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  1. Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectors

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  • Definition of weights in a linear combination of vectors#23802
  • Description of a basis for the null space of a matrix from the reduced row-echelon form.#23870
  • Description of a spanning set for the null space of a matrix from the reduced row-echelon form.#23869
  • Description of the Gram-Schmidt process#23935
  • Determinants#23714
  • Determinants and operations on matrices#23723
  • Determinants axiomatically#23732
  • Determine if a particular set of vectors in R^3 in linearly independent#23818
  • Determine if a particular set of vectors spans R^3#23807
  • Determine if a particular vector is in the span of a set of vectors#23808
  • Determine if a particular vector is in the span of a set of vectors in R^2#23809
  • Determine if a particular vector is in the span of a set of vectors in R^3#23810
  • Dimension#23836
  • Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.#23712
  • Each vector can be written uniquely as a linear combination of vectors from a given basis.#23987
  • Echelon matrices#23536
  • Eigenspaces#23683
  • Eigenvalues and eigenvectors#23680
  • Eigenvalues and operations on matrices#23688
  • Eigenvectors of a symmetric matrix with different eigenvalues are orthogonal.#23574
  • Eigenvectors with distinct eigenvalues are linearly independent.#23694
  • Elementary matrices#23556
  • Elementary matrices are invertible/nonsingular.#23560
  • Equation operations on a linear system give an equivalent system.#23425
  • Equivalence theorem for injective linear transformations: The columns of the matrix of T are linearly independent.#24086
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  • Aspen Summer 2016 - Entanglement Matters#1213
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