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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.
  • Matrix cancellation requires an invertibility or rank hypothesis
  • 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. Theorem describing matrix multiplication

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  • Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectorsClose match
  • Definition of matrix multiplication in terms of column vectorsClose match
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  • MultiplicationClose match
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  • Matrix-vector product is associativeClose match
  • Multiplication of block/partitioned matricesClose match
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  • Matrix addition is commutative and associative.Close match
  • Example of multiplying matricesClose match
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  • AdditionClose match
  • Operations on matricesClose match
  • Two matrices of the same size are equivalent if and only if they have the same rank.Close match
  • A matrix equation is equivalent to a linear systemClose match
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