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" C is the dot product of the ith row of A with the jth column of B. "
Fundamentals of Matrix Computations - 5. lappuse
autors: David S. Watkins - 2004 - 640 lapas
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Matrix Theory

David W. Lewis - 1991 - 308 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...
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The Student's Introduction to MATHEMATICA ®: A Handbook for Precalculus ...

Bruce F. Torrence, Eve A. Torrence - 1999 - 280 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...
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Linearity and the Mathematics of Several Variables

Stephen A. Fulling, Michael N. Sinyakov, Sergei V. Tischchenko - 2000 - 445 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....
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Linear Algebra and Differential Equations

Alexander Givental - 2001 - 132 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...
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Essential Matlab for Scientists and Engineers

Hahn, Brian D. Hahn - 2002 - 357 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...
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Differential Equations, Dynamical Systems, and an Introduction ..., 60. sējums

Morris W. Hirsch, Stephen Smale, Robert L. Devaney - 2004 - 417 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,...
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Semisupervised Learning for Computational Linguistics

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...
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A Course in Enumeration

Martin Aigner - 2007 - 565 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...
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Applications of Abstract Algebra with Maple and MATLAB, Second Edition

Richard Klima, Neil P. Sigmon, Ernest Stitzinger - 2006 - 528 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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