1 / 11

Overview

Overview. Definitions Basic matrix operations (+, -, x) Determinants and inverses. Some Definitions …. Zero Matrix Identity Matrix Diagonal Matrix. I A = A I = A. Basic Operations. Addition, Subtraction, Multiplication. Just add elements. Just subtract elements.

sani
Download Presentation

Overview

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. Overview • Definitions • Basic matrix operations (+, -, x) • Determinants and inverses

  2. Some Definitions … • Zero Matrix • Identity Matrix • Diagonal Matrix I A = A I = A

  3. Basic Operations • Addition, Subtraction, Multiplication Just add elements Just subtract elements Multiply each row by each column

  4. Try for the 2 matrices below Multiplication • Is AB = BA? Maybe, but maybe not! • Is multiplication commutative?

  5. AB = BA Multiplication Is AB = BA? Multiplication is NOT commutative

  6. Inverse of a Matrix • Identity matrix: AI = A • Some matrices have an inverse, such that:AA-1 = I

  7. Inverse of a 2x2 Matrix

  8. Matrix Inverse A-1 A = A-1 A = I Properties A-1 only exists if A is square (n x n)

  9. , so an inverse exists , so no inverse exists Determinant of a 2x2 Matrix • Used for inversion • If det(A) = 0, then A has no inverse • A matrix with no inverse is SINGULAR E.g.

  10. Inverse of a 2x2 Matrix • AA-1 = I • If det(A) = 0, then A has no inverse • A is SINGULAR det(A) E.g.

  11. The 2x2 identity matrix Inverse of a 2x2 Matrix • AA-1 = I • If det(A) = 0, then A has no inverse • A is SINGULAR

More Related