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Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part72

Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part72

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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 [ ] ' = A B A B 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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