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  • Operations on matrices

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  • Addition
  • Conjugation
  • Scalar multiplication
  • Row operations
  • Matrix-vector products
  • Multiplication
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  • Definition of matrix-scalar multiplication
  • Matrix-scalar multiplication is commutative
  • Scalar multiplication of matrices is associative and distributive
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  1. Scalar multiplication

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  • Definition of matrix-scalar multiplicationClose match
  • Scalar multiplication of matrices is associative and distributiveClose match
  • Matrix-scalar multiplication is commutativeClose match
  • Definition of vector-scalar multiplicationClose match
  • Definition of scalarClose match
  • Operations on matricesClose match
  • MultiplicationClose match
  • Matrix-vector productsClose match
  • Example of vector-scalar multiplication in R^2Close match
  • The conjugate of a matrix-scalar product is the product of the conjugates.Close match
  • Definition of scalar multiple of a linear transformationClose 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
  • A scalar multiple of a linear transformation is a linear transformationClose match
  • The eigenvalues of a scalar multiple of a matrix are the scalar multiples of the eigenvalues.Close match
  • AdditionClose match
  • The conjugate of vector-scalar multiplication in C^n is the product of the conjugates.Close match
  • Multiplying a row by a scalar multiplies the determinant by that scalar.Close match
  • If the product of a vector and a scalar is 0Close match
  • The matrix representation of a scalar multiple of linear transformations is the scalar multiple of the matrix.Close match
  • Eigenvalues and operations on matricesClose match

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