 | David W. Lewis - 1991 - 312 lapas
...(In shorthand notation the (ij)-entry is V ab .) kt, * kJ In other words the (ij)-entry of AB is the product of the i-th row of A with the j-th column of B, this product being as in the special case of Ьn and n*l matrices defined above. 1.1.5 Example Let... | |
 | Bruce F. Torrence, Eve A. Torrence - 1999 - 304 lapas
...35 -7 And we can multiply matrices. The i, jth entry of the product of the matrix a with the matrix b is the dot product of the ith row of a with the jth column of b. Multiplication is only possible if the number of columns of a is equal to the number of rows of... | |
 | Stephen A. Fulling, Michael N. Sinyakov, Sergei V. Tischchenko - 2000 - 466 lapas
...I 1 (This you should memorize immediately, or at least your fingers should.) Note also that (AB)ij is the dot product of the ith row of A with the jth column of B. Note that AB ^ BA in general. (They may not both be defined, because the shapes don't match up right.... | |
 | Alexander Givental - 2001 - 150 lapas
...where the entry is located. In these notations the entry Cij of the product matrix C = AB equals the product of the i-th row of A with the j-th column of B. Example, (b) The product DA (respectively AD) of the diagonal matrix D = -1 , with A = \ n 12 is... | |
 | Hahn, Brian D. Hahn - 2002 - 380 lapas
...The operation is written as C = AB, and the general element c^ of C is formed by taking the scalar product of the ith row of A with the jth column of B. (The scalar product of two vectors \ andy isx\yi +x22/2 + • • •• where x, and y, are the... | |
 | Morris W. Hirsch, Stephen Smale, Robert L. Devaney - 2004 - 433 lapas
..., . . . , xn) e R", we define the product AX to be the vector so that the ith entry in this vector is the dot product of the ith row of A with the vector X. Matrix sums are denned in the obvious way. If A = [«,)•] and B — [bjj] are nxn matrices,... | |
 | Steven Abney - 2007 - 320 lapas
...multiplication in terms of the individual entries of the product matrix: the (i, j)-th entry of AB is the dot product of the i-th row of A with the j-th column of B. But it is often better to consider the matrix- vector product as the more basic operation: y = Ax... | |
 | Martin Aigner - 2007 - 566 lapas
...the usual matrix product A -B for two such matrices. In order that this become meaningful, the inner product of the i-th row of A with the j-th column of В must consist of finitely many non-zero summands. The most important case in which this happens is... | |
 | Richard Klima, Neil P. Sigmon, Ernest Stitzinger - 2006 - 536 lapas
...contain both a; and a,-. Since the entry in the ith row and jth column of the matrix AAT can be viewed as the dot product of the ith row of A with the jth row of A, then AAT is as follows, where / is the vxv identity matrix, and J is avxv matrix containing... | |
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C is the dot product of the ith row of A with the jth column of B. 