premultiplyv.
/priːˈmʌltᵻplʌɪ/, U.S. /ˌpriˈməltəˌplaɪ/ Mathematics.
transitive. To multiply (a function, matrix, group element, etc.) by (or as) a preceding factor, esp. when the operation is non-commutative. Also intransitive. Cf. postmultiply v.
ΘΚΠ
the world > relative properties > number > arithmetic or algebraic operations > perform arithmetic or algebraic operations [verb (transitive)] > multiply > by a factor
postmultiply1861
premultiply1861
normalize1900
norm1914
1861 Philos. Trans. (Royal Soc.) 151 312 These numbers will remain unchanged, when the given matrix is premultiplied by any unit-matrix, and post-multiplied by any matrix whatsoever.
1946 H. H. Goldstine in Moore School Lect. (1985) 141 In this case we pre-multiply by the transpose of the coefficient matrix.
1978 Nature 20 Apr. 740/1 We are told, as though it were surprising, that pre- and post-multiplying a matrix by the matrix of its eigenvectors produces a diagonal matrix.
1991 N. Higham in C. Bondi New Applic. Math. ii. 53 By analogy with the scalar case, we would like to solve the system of equations Ax = b by pre-multiplying by an n × n matrix A−1 to obtain x = A−1Ax = A−1b.
Derivatives
premultipliˈcation n.
ΘΚΠ
the world > relative properties > number > arithmetic or algebraic operations > [noun] > multiplication
multiplicationa1393
multiplying?a1400
ductionc1430
leadingc1430
composition1557
practice1562
postmultiplication1861
premultiplication1861
1861 Philos. Trans. (Royal Soc.) 151 316 Let that matrix be reduced by premultiplication with a unit-matrix.
1947 S. A. Stigant Mod. Electr. Engin. Math. iv. 63 The first method consists of the pre-multiplication and post-multiplication of [A], suitably partitioned, by a series of matrices.
1987 A. R. Collar & A. Simpson Matrices & Engin. Dynamics (BNC) 26 Postmultiplication of any matrix C by the conformable J matrix reverses the order of the columns of C while premultiplication by J reverses the order of the rows.
This entry has been updated (OED Third Edition, March 2007; most recently modified version published online March 2022).
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