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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. Matrix cancellation requires an invertibility or rank hypothesis

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  • Matrix inverses are unique: if A and B are square matricesClose match
  • Matrix multiplication is not commutative in general.Close match
  • Matrix multiplication is associative.Close match
  • InverseClose match
  • Matrix conjugation is an involution.Close match
  • If a square matrix has a one-sided inverseClose match
  • Matrix-scalar multiplication is commutativeClose match
  • Equivalence theorem for nonsingular matrices: the matrix A has a right inverse.Close match
  • Matrix multiplication is distributive over matrix addition.Close match
  • For n-by-n invertible matrices A and BClose match
  • Theorem describing matrix multiplicationClose match
  • Equivalence theorem for nonsingular matrices: the matrix A has an inverse.Close match
  • Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectorsClose match
  • Equivalence theorem for nonsingular matrices: the matrix A has a left inverse.Close match
  • Example of multiplying nonsquare matricesClose match
  • Example of multiplying 2x2 matricesClose match
  • Definition of matrix-scalar multiplicationClose match
  • Example of multiplying 3x3 matricesClose match
  • Determinants multiply: det(AB) = det(A)det(B)Close match
  • Matrix addition is commutative and associative.Close match

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