cs440-lec3-algebra

# cs440-lec3-algebra - Introduction to Artificial...

This preview shows pages 1–6. Sign up to view the full content.

Introduction to Artificial Intelligence Lecture #3: Matrix Algebra & Probability UIUC CS 440 / ECE 448 Professor: Eyal Amir Spring Semester 2008

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Last Time Propositional Logic Propositional symbols / variables Formulas Connectives: a b a b ¬ a a b Truth Assignment, Truth tables, Satisfying assignments (models) Logical Entailment ( M |= ϕ ψ |= ϕ ) Newsgroup: CNF, Validity, de-morgan
Today: Matrix Algebra Matrix Algebra: Vector Spaces: addition, multiplication, dot product, metrics, norms, angles Matrices: addition, multiplication, eigen vectors, eigen values, inverse, determinant Properties: rank, positive definite, null space

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Representing Knowledge: Vectors Examples: Position of a robot <10,9> Position of a robot arm <angle1,angle2,…> Truth assignment <0,1,1,0> for <x1,x2,x3,x4> Vector of values Vector of variables
Vector Spaces A Field F is a set of elements U, and binary functions +,* and unary operator -. R

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/04/2008 for the course CS 440 taught by Professor Eyalamir during the Spring '08 term at University of Illinois at Urbana–Champaign.

### Page1 / 18

cs440-lec3-algebra - Introduction to Artificial...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online