# week08 - Rutgers University School of Engineering Fall 2011...

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Rutgers University School of Engineering Fall 2011 14:440:127 - Introduction to Computers for Engineers Sophocles J. Orfanidis ECE Department [email protected] week 8

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Week 1 - Basics – variables, arrays, matrices, plotting (ch. 2 & 3) Week 2 - Basics – operators, functions, program flow (ch. 2 & 3) Week 3 - Matrices (ch. 4) Week 4 - Plotting – 2D and 3D plots (ch. 5) Week 5 - User-defined functions (ch. 6) Week 6 - Input-output processing (ch. 7) Week 7 - Program flow control & relational operators (ch. 8) Week 8 - Matrix algebra – solving linear equations (ch. 9) Week 9 - Strings, structures, cell arrays (ch. 10) Week 10 - Symbolic math (ch. 11) Week 11 - Numerical methods – data fitting (ch. 12) Week 12 – Selected topics Weekly Topics Textbook: H. Moore, MATLAB for Engineers , 2 nd ed., Prentice Hall, 2009
Matrix Algebra • dot product • matrix-vector multiplication • matrix-matrix multiplication • matrix inverse • solving linear systems • least-squares solutions • determinant, rank, condition number • vector & matrix norms •e x a m p l e s • electric circuits • temperature distributions The dot product is the basic operation in matrix-vector and matrix-matrix multiplications

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Operators and Expressions operation element-wise matrix-wise addition + + subtraction -- multiplication .* * division ./ / left division .\ \ exponentiation .^ ^ transpose w/o complex conjugation . ' transpose with complex conjugation ' >> help / >> help precedence used in matrix algebra operations
>> A = [1 2; 3 4] A = 1 2 3 4 >> [A, A.^2; A^2, A*A] % form sub-blocks ans = 1 2 1 4 3 4 9 16 7 10 7 10 % note A^2 = A*A 15 22 15 22 >> B = 10.^A; >> [B, log10(B)] ans = 10 100 1 2 1000 10000 3 4

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>> A = [1 2 3; 2 0 4; 0 8 5] A = 1 2 3 2 0 4 0 8 5 >> size(A) % [N,M] = size(A), NxM matrix ans = 3 3 matrix indexing convention
math notations MATLAB notation dot product a , b must have the same dimension

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math notations MATLAB notation dot product for complex-valued vectors complex-conjugate transpose, or, hermitian conjugate of a for real-valued vectors, the operations ' and .' are equivalent
>> a = [1; 2; -3]; b = [4; -5; 2]; >> a'*b ans = -12 >> dot(a,b) % built-in function ans = % same as sum(a.*b) -12

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matrix-vector multiplication combine three dot product operations into a single matrix-vector multiplication
matrix-vector multiplication combine three dot product operations into a single matrix-vector multiplication A x = b

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matrix-matrix multiplication combine three matrix-vector multiplications into a single matrix-matrix multiplication
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## This document was uploaded on 11/04/2011 for the course ENGINEERIN 440 at Rutgers.

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week08 - Rutgers University School of Engineering Fall 2011...

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