 | National Research Council (U.S.) - Research - 1922 - 526 pages
...th£orie des nombree, Paris, 1913. whose elements are integral numbers of an algebraic field R. If the number of columns of A is equal to the number of rows of B, we obtain by multiplication a matrix C=(S a,j blk) having as many rows as A i and as many columns as... | |
 | National Research Council (U.S.) - Research - 1922 - 528 pages
...1386-9). ' Math Annalm, 71, 1912, 328-354. whose elements are integral numbers of an algebraic field R. If the number of columns of A is equal to the number of rows of B, we obtain bv multiplication a matrix C=(2 aa bit) having as many rows as A t and as many columns as... | |
 | A. G. Howson - Mathematics - 1972 - 254 pages
...corresponding to the matrix A. The matrix product AB of the matrices A and B is not defined unless the number of columns of A is equal to the number of rows of B (is equal to the dimension of V). The existence of the product AB will not therefore imply the existence... | |
 | The Analytic Sciences Corporation - Computers - 1974 - 388 pages
...the matrix AB = C=[cy] (2.1-15) The product AB is defined only when A and B are conformable, that is, the number of columns of A is equal to the number of rows of B. Where A is m X p and B is p X n, the product matrix [c¡jj ñas m rows and n columns and c¡j is gifen... | |
 | L. Meirovitch - Mathematics - 1980 - 462 pages
...+ ainbni = £ aikbki ( 1 .37) It is clear from the above that the matrix product is defined only if the number of columns of A is equal to the number of rows of B. In this case. the matrices A and B are said to be conformable in the order stated. The matrix product... | |
 | James M. Ortega - Mathematics - 1987 - 278 pages
...a linear combination of the matrices A,. The product AB of two matrices A and B is defined only if the number of columns of A is equal to the number of rows of B. Then if A is nxp and B is pxm, the product C = /\B is an nxm matrix C whose ij element is given by... | |
 | James M. Ortega - Mathematics - 1987 - 278 pages
...a linear combination of the matrices A,. The product AB of two matrices A and B is defined only if the number of columns of A is equal to the number of rows of B. Then if A is n x p and B is p xm, the product C = /\B is an n xm matrix C whose ij element is given... | |
 | Leonid Mirsky - Mathematics - 1990 - 468 pages
...however, we break fresh ground. DEFINITION 3.3.3. Suppose that A is an lxm matrix and B an mxn matrix, so that the number of columns of A. is equal to the number of rows of B. Then the matrix product AB is the lxn matrix defined by the relations (AB)tf = , = t-1 ; j = 1,....n).... | |
 | G.S. Christensen, S.A. Soliman, R. Nieva - Mathematics - 1990 - 266 pages
...by a: 2.2.2.3. Multiplication of Two Matrices The product AB of matrices A and B is defined only if the number of columns of A is equal to the number of rows of B; BA and B are then said to be conformable for multiplication. The dimension of the resulting product... | |
 | William Brown - Mathematics - 1991 - 338 pages
...why block multiplication works. Remember that a product of two matrices A and B is defined only when the number of columns of A is equal to the number of rows of B. This fact allows only certain types of partitions for block multiplication. We will build up to the... | |
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AB is defined if and only if the number of columns of A is equal to the number of rows of B... 
