Conformable matrix

In mathematics, a matrix is conformable if its dimensions are suitable for defining some operation (e.g. addition, multiplication, etc.).[1]

Examples

  • If two matrices have the same dimensions (number of rows and number of columns), they are conformable for addition.
  • Multiplication of two matrices is defined if and only if the number of columns of the left matrix is the same as the number of rows of the right matrix. That is, if A is an m × n matrix and B is an s × p matrix, then n needs to be equal to s for the matrix product AB to be defined. In this case, we say that A and B are conformable for multiplication (in that sequence).
  • Since squaring a matrix involves multiplying it by itself (A2 = AA) a matrix must be m × m (that is, it must be a square matrix) to be conformable for squaring. Thus for example only a square matrix can be idempotent.
  • Only a square matrix is conformable for matrix inversion. However, the Moore–Penrose pseudoinverse and other generalized inverses do not have this requirement.
  • Only a square matrix is conformable for matrix exponentiation.
gollark: I specified that you couldn't have a well-typed generic map earlier, I think.
gollark: You can use interface{}, yes, but it's:- overcomplicated- slow- unsafe
gollark: I think the second one is more valuable.
gollark: I mean, the for loop way makes... the underlying stuff clearer, but the map way makes your intentions clearer.
gollark: ???

See also

References

  1. Cullen, Charles G. (1990). Matrices and linear transformations (2nd ed.). New York: Dover. ISBN 0486663280.
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