conformable

　 　

WordNet

1. quick to comply; "I have been to you a true and humble wife, at all times to your will conformable"-Shakespeare
2. not correspondent; "a description unconformable to previous accounts"

PrepTutorEJDIC

1. 一致した,適合した・準拠した

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/06/20 05:48:26」(JST)

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"Conformable" redirects here. For the topic in geology, see Unconformity.

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

Examples

• If the sum of two matrices is defined, that is, if they have the same order, then they are said to be 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.

References

See also

• Linear algebra

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