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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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101–125 of 715 nodes
  • Definition of 0 matrix#23458
  • Definition of 0/trivial subspace#23964
  • Definition of 0 vector#23784
  • Definition of adjoint (conjugate transpose)#23506
  • Definition of adjugate/classical adjoint of a matrix#23748
  • Definition of (algebraic) multiplicity of an eigenvalue#23696
  • Definition of a lower triangular matrix#23563
  • Definition of angle between vectors#23915
  • Definition of an upper triangular matrix#23562
  • Definition of applying a polynomial to a linear transformation#24048
  • Definition of applying a polynomial to a square matrix#23700
  • Definition of augmented matrix (of a linear system)#23755
  • Definition of automorphism of a vector space#24007
  • Definition of a vector being orthogonal to a subspace#23919
  • Definition of band matrix#23593
  • Definition of basic/dependent/leading variable in a linear system#23442
  • Definition of basis of a vector space (or subspace)#23829
  • Definition of block diagonal matrix#23570
  • Definition of block/partitioned matrix#23568
  • Definition of change of coordinates matrix between two bases#23995
  • Definition of change-of-coordinates matrix relative to a given basis of R^n (or C^n)#23832
  • Definition of characteristic equation of a matrix#23702
  • Definition of characteristic polynomial of a linear transformation#24044
  • Definition of characteristic polynomial of a matrix#23701
  • Definition of Cholesky decomposition#23629
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  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

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