Chapter 2 Section 4
... A Repeat of the WARNING • If the system of equations has the either an infinite number of solutions or no solutions, then there will not be an inverse matrix ( i.e. The ERR: SINGULAR MAT error in the calculator). Unfortunately the error message will not tell you which of the two situations caused t ...
... A Repeat of the WARNING • If the system of equations has the either an infinite number of solutions or no solutions, then there will not be an inverse matrix ( i.e. The ERR: SINGULAR MAT error in the calculator). Unfortunately the error message will not tell you which of the two situations caused t ...
1 Eigenvalues and Eigenvectors
... Similar Matrices 1. Definition: The n × n matrices A and B are said to be similar if there is an invertible n × n matrix P such that A = P BP −1 . 2. Similar matrices have at least one useful property, as seen in the following theorem. See page 315 for a proof of this theorem. 3. Theorem 4: If n × n ...
... Similar Matrices 1. Definition: The n × n matrices A and B are said to be similar if there is an invertible n × n matrix P such that A = P BP −1 . 2. Similar matrices have at least one useful property, as seen in the following theorem. See page 315 for a proof of this theorem. 3. Theorem 4: If n × n ...
p:texsimax -1û63û63 - Cornell Computer Science
... things) at each step we need to compute the m-by-n2 Jacobian J of the vector-valued function φ(A). Suppose an ODE solver is used to generate fk (A)b ≈ x(tk ) for k = 1:m. If each of these vectors requires O(n2 ) flops to compute, then a φ-evaluation costs O(mn2 ) flops and a finite-difference approximat ...
... things) at each step we need to compute the m-by-n2 Jacobian J of the vector-valued function φ(A). Suppose an ODE solver is used to generate fk (A)b ≈ x(tk ) for k = 1:m. If each of these vectors requires O(n2 ) flops to compute, then a φ-evaluation costs O(mn2 ) flops and a finite-difference approximat ...
