Английская Википедия:Conformable matrix

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

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 Шаблон:Math is an Шаблон:Math matrix and Шаблон:Math is an Шаблон:Math matrix, then Шаблон:Math needs to be equal to Шаблон:Math for the matrix product Шаблон:Math to be defined. In this case, we say that Шаблон:Math and Шаблон:Math are conformable for multiplication (in that sequence).
• Since squaring a matrix involves multiplying it by itself (Шаблон:Math) a matrix must be Шаблон:Math (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.

See also

• Linear algebra

References

Шаблон:Matrix-stub