MAE 07 UCSD

1 MAE290a midterm (2007) Im so blue without LU. 75 minutes, closed book, no calculators, one page of notes allowed. 1. Orthogonalize and normalize the columns of 3 6 9 A = 4 8 12 02 1 using the Gram-Schmidt procedure, and determine by hand an ortho

1 MAE290a nal (2007) 3 hours, closed book, no calculators, two pages of notes allowed. 1. Reections and rotations of a vector in Rn Recall the denition H = I wwH where = 2, w= x + e1 , x + e1 = Sign(x1 ) x , and the representative example matrix

1 MAE290a nal solutions (2007) 1. Reections and rotations of a vector in Rn (a) H is the Householder reector matrix, and G is the Givens rotation matrix. (b) H H X costs 4n2 ops to compute, and GH X costs 6n ops to compute. 1 0 0 1 (c) H = I 2

1 MAE290a nal solutions (2007) 1. Reections and rotations of a vector in Rn (a) H is the Householder reector matrix, and G is the Givens rotation matrix. (b) H H X costs 4n2 ops to compute, and GH X costs 6n ops to compute. 1 0 0 1 (c) H = I 2

1 MAE290a midterm (2007) Im so blue without LU. 75 minutes, closed book, no calculators, one page of notes allowed. 1. Orthogonalize and normalize the columns of 3 6 9 A = 4 8 12 02 1 using the Gram-Schmidt procedure, and determine by hand an ortho

1 MAE290a nal (2007) 3 hours, closed book, no calculators, two pages of notes allowed. 1. Reections and rotations of a vector in Rn Recall the denition H = I wwH where = 2, w= x + e1 , x + e1 = Sign(x1 ) x , and the representative example matrix