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Numerical-Computing

# Numerical-Computing - ASSIGNMENTS FOR NUMERICAL COMPUTATION...

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ASSIGNMENTS FOR NUMERICAL COMPUTATION MAN V. M. NGUYEN, PH.D. ——————————————————————————— Part I: Matrices Computation Assignment IA: Vector Products and Transpose For real matrices, the transpose operation interchanges a i,j and a j,i . MAT- LAB uses the apostrophe operator (’) to perform a complex conjugate trans- pose , resulting a matrix called adjoint matrix ; and the dot-apostrophe operator (.’) to transpose without conjugation. For matrices containing all real elements, the two operators return the same result. For a complex vector or matrix, z , the quantity z 0 not only transposes the vector or matrix, but also converts each complex element to its complex conjugate. That is, the sign of the imaginary part of each complex element is changed. Multiplying Matrices: reflects composition of the underlying linear trans- formations and allows compact representation of systems of simultaneous linear equations. If A is m -by- p and B is p -by- n , their product C = AB is m -by- n . In MATLAB, try the followings B = magic(3); X = B’ z = [1+2i 7-3i 3+4i; 6-2i 9i 4+7i]; z’; z.’ A = pascal(3); B = magic(3); X = A*B; Y = B*A The Identity Matrix: I = eye(3,3) Date : September 6, 2010 Email: [email protected] .

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