Conformable matrix
Encyclopedia
In mathematics
, a matrix
is conformable if its dimensions are suitable for defining some operation (e.g. addition, multiplication, etc.).
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
is conformable if its dimensions are suitable for defining some operation (e.g. addition, multiplication, etc.).
Examples
- In order to be conformable to addition, matrices need to have the same dimensions. Thus A, B and C all must have dimensions m × n in the equation
- for some fixed m and n.
- For matrix multiplicationMatrix multiplicationIn mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix. If A is an n-by-m matrix and B is an m-by-p matrix, the result AB of their multiplication is an n-by-p matrix defined only if the number of columns m of the left matrix A is the...
, consider the equation
- If A has dimensions m × n, then B has to have dimensions n × p for some p, so that C will have dimensions m × p.