COMS 421 CRIB SHEET

# COMS 421 CRIB SHEET - COMS 421 CRIB SHEET, PRELIM 1,...

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COMS 421 CRIB SHEET, PRELIM 1, 09/20/2004 Hallmarks of scientific computing: 1. Compute with real numbers 2. 3. Very large problems Three branches of scientific computing: 1. Numerical linear algebra 2. Differential equations 3. Optimization Linear Algebra Review: Subspace of R n is a set S in R n such that (a) Ø is in S and (b), S y x 2200 ) , ( and R 2200 ) , ( β α , S y x + . n R x is a Linear Combination of v 1 …v n if there exists B 1 B n s.t. x = B 1 v 1 + … + B n v n . The Span of {v 1 … v n } is all vectors in R n that are linear combinations of {v 1 … v n }. A span is a subspace. Vectors v 1 … v n are Linearly Independent if the only way to express 0 as a linear combination is with 0s for coefficients. {v 1 … v k } in S form a Basis of S if they (a) span S, and (b) are linearly independent. Standard basis: {e 1 … e 2 }. Thm:

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## This note was uploaded on 10/08/2010 for the course NE 112 taught by Professor Vanelli during the Spring '10 term at Waterloo.

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COMS 421 CRIB SHEET - COMS 421 CRIB SHEET, PRELIM 1,...

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