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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 distance between vectors#24091
  • Definition of domain of a linear transformation#23840
  • Definition of echelon form of a linear system#23422
  • Definition of (echelon matrix/matrix in (row) echelon form)#23539
  • Definition of eigenspace of a linear transformation#24050
  • Definition of eigenspace of a matrix#23684
  • Definition of eigenvalue/characteristic value of a linear transformation#24042
  • Definition of eigenvalue of a matrix#23681
  • Definition of eigenvector/characteristic vector of a linear transformation#24043
  • Definition of eigenvector of a matrix#23682
  • Definition of elementary matrix#23557
  • Definition of entry/component of a vector#23783
  • Definition of equality of matrices#23459
  • Definition of equality of vectors#23785
  • Definition of equation operations on a linear system#23424
  • Definition of equivalent matrices#23604
  • Definition of equivalent systems of linear equations#23426
  • Definition of extended reduced row echelon form of a matrix#23550
  • Definition of free/independent variable in a linear system#23443
  • Definition of generalized inverse of a matrix#23534
  • Definition of generalized kernel/null space of linear transformation#24060
  • Definition of generalized range space of a linear transformation#24039
  • Definition of geometric multiplicity of an eigenvalue#23697
  • Definition of Gram-Schmidt process#24093
  • Definition of Hermitian/self-adjoint matrix#23597
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