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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 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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  • Geometric properties of linear transformations#23851
  • Geometric properties of linear transformations on R^2#23853
  • Geometric properties of R^n (or C^n)#23795
  • Hermitian matrices#23596
  • Hermitian matrices have real eigenvalues.#23711
  • Homogeneous linear systems are consistent.#23434
  • If a matrix has both a left and a right inverse#23519
  • If a set of vectors contains the 0 vector#23825
  • If a set of vectors in R^n (or C^n) contains more than n elements#23827
  • If a square matrix has a one-sided inverse#23520
  • If a vector space has dimension n#23838
  • If the product of a vector and a scalar is 0#23962
  • If two matrices have equal products with all vectors#23484
  • Ill-conditioning is measured by relative distance to singularity#23749
  • Inner products#24087
  • Inner products in coordinate spaces#23894
  • Invariant direct sums give block diagonal operator matrices#24053
  • Inverse#23514
  • Isomorphic vector spaces have the same dimension.#24004
  • Isomorphism#24000
  • Least squares#23945
  • Linear algebra#23410
  • Linear Algebra content audit and completionArchived#29496
  • Linear Algebra practice problems with worked solutions#37116
  • Linear Algebra study guide, conventions and references#37114
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