cs440-lec3-algebra

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

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Introduction to Artificial Intelligence Lecture #3: Matrix Algebra & Probability UIUC CS 440 / ECE 448 Professor: Eyal Amir Spring Semester 2008
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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
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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
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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
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Vector Spaces A Field F is a set of elements U, and binary functions +,* and unary operator -. R
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cs440-lec3-algebra - Introduction to Artificial...

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