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5 Review Linear Algebra (1)

# 5 Review Linear Algebra (1) - IEE 598 5(I.1 Review Linear...

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IEE 598 - 5 (I.1) Review Linear Algebra Muhong Zhang DEPARTMENT OF INDUSTRIAL ENGINEERING Feb. 09, 2010

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Review: Linear Algebra Definition: ¯ x is said to be a linear combination of x 1 , x 2 , ..., x k R n if ¯ x = k i = 1 λ i x i , λ i R , i = 1 , ..., k . Definition: ¯ x is said to be an affine combination of x 1 , x 2 , ..., x k R n if ¯ x = k i = 1 λ i x i , k i = 1 λ i = 1, λ i R n , i = 1 , ..., k . Definition: ¯ x is said to be a conic combination of x 1 , x 2 , ..., x k R n if ¯ x = k i = 1 λ i x i , λ i 0, i = 1 , ..., k . Definition: ¯ x is said to be a convex combination of x 1 , x 2 , ..., x k R n if ¯ x = k i = 1 λ i x i , k i = 1 λ i = 1, λ i 0, i = 1 , ..., k . Zhang IEE 376 Introduction to OR 2 / 7
Review: Linear Algebra Definition: The span of S = { x 1 , x 2 , ..., x k } ⊆ R n is the set of all linear combination of x 1 , x 2 , ..., x k . We denote it as span ( S ) . Definition: The affine hull of S = { x 1 , x 2 , ..., x k } ⊆ R n is the set of all affine combination of x 1 , x 2 , ..., x k . We denote it as aff ( S ) .

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5 Review Linear Algebra (1) - IEE 598 5(I.1 Review Linear...

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