ass5 - ASSIGNMENT 5 MATH 270, WINTER 2010. DUE: 5PM, APRIL...

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ASSIGNMENT 5 MATH 270, WINTER 2010. DUE: 5PM, APRIL 7, 2010. Assignments must have your name, student number, course number and TA’s name on the first page. Please submit them by placing them in the box marked “Assignments” outside the Maths Office (Burn- side Hall, 10th floor). Show all working and justifications! (1) The matrices A = 1 4 1 - 1 1 - 1 - 1 1 - 1 1 1 - 1 1 - 1 - 1 1 - 1 1 and B = 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 belong to which of the following classes: Defective? Factorisable as A = LU or B = LU ? Factorisable as A = QR or B = QR ? Invertible? Normal? Permutation? Projection? Self-adjoint? Skew-symmetric? Unitary? Give reasons in each case! [ Total: 10 marks ] (2) (a) Show that a unitary matrix U must have | det ( U ) | = 1. Give an example of a unitary matrix whose determinant is not 1. [ 2 marks ] (b) If a diagonalisable matrix A has | det ( A ) | = 1, must A be unitary? [ 1 mark
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This note was uploaded on 05/06/2010 for the course MATH MATH270 taught by Professor Ridout during the Winter '10 term at McGill.

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ass5 - ASSIGNMENT 5 MATH 270, WINTER 2010. DUE: 5PM, APRIL...

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