1 / 11

Applied Linear Algebra

Applied Linear Algebra. Review. LU Factorization. If a square matrix can strict upper triangular form, U, without interchanging any rows, then A can be factored as A=LU, where L is a low triangular matrix. Ax= b L(Ux )= b Solve Ly= b then y = Ux. Elementary Matrices.

deacon-bean
Télécharger la présentation

Applied Linear Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Applied Linear Algebra Review

  2. LU Factorization • If a square matrix can strict upper triangular form, U, without interchanging any rows, then A can be factored as A=LU, where L is a low triangular matrix. Ax=b L(Ux)=b Solve Ly=b then y=Ux

  3. Elementary Matrices • An elementary matrix of type I is a matrix obtained by interchanging two rows of I

  4. Elementary Matrices Row 1 and Row 2 are switched! Column 1 and Column 2 are switched!

  5. Elementary Matrices • An elementary matrix of type I is a matrix obtained by interchanging two rows of I • An elementary matrix of type II is a matrix obtained by multiplying a row of I by a nonzero constant

  6. Elementary Matrices Row 2 is multiplied by 3! Column 2 is multiplied by 3!

  7. Elementary Matrices • An elementary matrix of type I is a matrix obtained by interchanging two rows of I • An elementary matrix of type II is a matrix obtained by multiplying a row of I by a nonzero constant. • An elementary matrix of type III is a matrix obtained from I by adding a multiple of one row to another row.

  8. Elementary Matrices 4 times Row 3 is added to Row 1 4 times Column 1 is added to column 3

  9. Change of Basis

  10. Change of Basis

  11. Gram-Schmidt Orthonomalization Process

More Related