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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.

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Overview

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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

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