MATH 247 Study Guide - Final Guide: Triangular Matrix, Bilinear Form, Matrix Exponential
24 Dec 2018
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Main topics: triangularization, matrix exponentials, odes, di erence equations, orthogonal- ity, bilinear form, inner product. Aim: given a mat(n n, c), nd a triangular or upper triangular matrix t similar to a. Recall from last lecture that this was a recursive algorithm. We nd one eigenvalue 1, and its corresponding eigenvector v1. Extend this v1 to a basis v1, , vn of cn. Recall that this is a change of basis and is therefore a coordinate transformation: B where u cn 1 and b m at (n 1, n 1, c). Because this is a recursive algorithm, we apply the same exact idea to b to a matrix we call c. perform this algorithm n 1 times until we obtain something in upper triangular form. We can nd these either using the math 133 way or by using the algorithm from last class. Usually the initial vector x0 is provided: < 1, 0, 0 >.
