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Multiplication, Division, and Exponentiation Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition A 19 Copyright © Orchard Publications In Section A.2, the arrays , such a those that contained the coefficients of polynomi- als, consisted of one row and multiple columns, and thus are called row vectors . If an array has one column and multiple rows, it is called a column vector . We recall that the elements of a row vector are separated by spaces. To distinguish between row and column vectors, the elements of a column vector must be separated by semicolons. An easier way to construct a column vector, is to write it first as a row vector, and then transpose it into a column vector. MATLAB uses the single quotation character ( ) to transpose a vector. Thus, a column vector can be written either as b=[ 1; 3; 6; 11] or as b=[ 1 3 6 11]' As shown below, MATLAB produces the same display with either format. b=[ 1; 3; 6; 11] b = -1 3 6 11 b=[ 1 3 6 11]' % Observe the single quotation character (‘) b = -1 3 6 11 We will now define Matrix Multiplication and Element by Element multiplication. 1 . Matrix Multiplication (multiplication of row by column vectors) Let and be two vectors. We observe that is defined as a row vector whereas is defined as a col- umn vector, as indicated by the transpose operator ( ). Here, multiplication of the row vector by the column vector , is performed with the matrix multiplication operator (*). Then, (A.5) a b c [] A a 1 a 2 a 3 a n = B b 1 b 2 b 3 b n ' = AB A*B a 1 b 1 a 2 b 2 a 3 b 3 a n b n +++ + gle value sin ==
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Appendix A Introduction to MATLAB® A 20 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications For example, if and the matrix multiplication produces the single value 68, that is, and this is verified with the MATLAB script A=[1 2 3 4 5]; B=[ 2 6 3 8 7]'; A*B % Observe transpose operator (‘) in B ans = 68 Now, let us suppose that both and are row vectors, and we attempt to perform a row by row multiplication with the following MATLAB statements. A=[1 2 3 4 5]; B=[ 2 6 3 8 7]; A*B % No transpose operator (‘) here When these statements are executed, MATLAB displays the following message: ??? Error using ==> * Inner matrix dimensions must agree. Here, because we have used the matrix multiplication operator (*) in A*B , MATLAB expects vector to be a column vector, not a row vector. It recognizes that is a row vector, and warns us that we cannot perform this multiplication using the matrix multiplication operator (*). Accordingly, we must perform this type of multiplication with a different operator. This operator is defined below.
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This note was uploaded on 11/20/2009 for the course EE EE 102 taught by Professor Bar during the Fall '09 term at UCLA.

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