STAT312 Lecture Notes - Triangular Matrix, Block Matrix, Lu Decomposition

51 views5 pages

Document Summary

The inverse of a non-singular block matrix can be computed by. This is established merely by multiplying the orig- inal block matrix by its alleged inverse, and verify- ing that the product is indeed the identity matrix. This is a very useful result if one of p or q is much smaller than the other, which in turn has special struc- ture which makes it easy to invert. Another consequence of (10. 1) is: if a is an matrix and b is a matrix ( ), then the eigenvalues of ba are those of ab together with. Proof: using the two formulas for the determi- nant of a block matrix, we obtain zeros. det i. | i and = |i | | i. 63 ( ) = 0 for ab together with and the roots of the characteristic equation. 0 for ba are those of the characteristic equation.

Get access

Grade+20% off
$8 USD/m$10 USD/m
Billed $96 USD annually
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
40 Verified Answers
Class+
$8 USD/m
Billed $96 USD annually
Class+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
30 Verified Answers

Related textbook solutions