Lecture18 - Engineering Analysis ENG 3420 Fall 2009 Dan C...

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Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00

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2 Lecture 18 Lecture 18 ± Last time: ² Linear algebra functions in Matlab ² Vector products ² Tensor product of two matrices ² Norm and matrix condition number ² Characteristic equation, eigenvectors, eigenvalues ± Today: ² Midterm: solutions and discussions ² More on characteristic equation, eigenvectors, eigenvalues ² The inverse of a matrix ² More on ± LU Factorization ± Cholesky decomposition ± Next Time (Chapter 12) ² Gauss-Siedel
The inverse of a square ± If [ A ] is a square matrix, there is another matrix [ A ] -1 , called the inverse of [ A ], for which [ A ][ A ] -1 =[ A ] -1 [ A ]=[I] ± The inverse can be computed in a column by column fashion by generating solutions with unit vectors as the right-hand-side constants: A [] x 1 {} = 1 0 0 A x 2 = 0 1 0 A x 3 = 0 0 1 A 1 = x 1 x 2 x 3

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Canonical base of an n-dimensional vector space 100……000 010……000 001……000 …………….
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Lecture18 - Engineering Analysis ENG 3420 Fall 2009 Dan C...

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