5 Review Linear Algebra (1)

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

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Unformatted text preview: IEE 598 - 5 (I.1) Review Linear Algebra Muhong Zhang DEPARTMENT OF INDUSTRIAL ENGINEERING Feb. 09, 2010 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 i x i , 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 i x i , k i = 1 i = 1, 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 i x i , 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 i x i , k i = 1 i = 1, 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 ) ....
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5 Review Linear Algebra (1) - IEE 598 - 5 (I.1) Review...

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