Test2 - • Vector Space Axioms(a Vector Addition(b Scalar...

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Unformatted text preview: • Vector Space Axioms (a) Vector Addition (b) Scalar Multiplication (c) Additive Commuta- tivity (d) Additive Associativity (e) Additive Identity (f) Multiplicative Assoc. (g) Multiplicative Iden- tity (h) Proper Distribution • L-Norms for C [ a,b ] (a) L 1 = divides.alt0divides.alt0 f divides.alt0divides.alt0 1 = ∫ b a divides.alt0 f ( x )divides.alt0 dx (b) L 2 = divides.alt0divides.alt0 f divides.alt0divides.alt0 2 = parenleft.alt2 ∫ b a divides.alt0 f ( x )divides.alt0 2 dx parenright.alt2 1 slash.left 2 (c) L ∞ = divides.alt0divides.alt0 f divides.alt0divides.alt0 ∞ = max x ∈[ a,b ] divides.alt0 f ( x )divides.alt0 • Inner Product for C [ a,b ]- < f,g >= ∫ b a f ( x ) g ( x ) dx • Subspace – With vector space V and a subset, S , of V , S is a subspace of V if S is also a vector space. To show this S must be closed under vector addition, scalar multiplication and be nonempty. (Theorem 3.14) – If S and T are subspaces of a vector space of V then S ⋂ T is a subspace of...
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This note was uploaded on 01/23/2012 for the course MATH 3012 taught by Professor Costello during the Fall '08 term at Georgia Tech.

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