Slides_2010_01_22 - Applied linear algebra and numerical...

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Unformatted text preview: Applied linear algebra and numerical analysis Session 8 Prof. Ulrich Hetmaniuk Department of Applied Mathematics January 22, 2010 Trivia What is the Fields medal? Trivia What is the Fields medal? • Often described as the Nobel Prize of Mathematics. • Awarded every 4 years since 1936. • Recipient is at most 40 years old. Trivia What is the Fields medal? • Often described as the Nobel Prize of Mathematics. • Awarded every 4 years since 1936. • Recipient is at most 40 years old. • Monetary award: $15,000 (Noble Prize ≈ $1M) Exercise Check whether the following operator is linear: • O : C ( R , R ) → C ( R , R ) such that O ( f )( x ) = xf ( x ) ∀ x ∈ R . Set of real matrices Definition The set of all real matrices with m rows and n columns is R m × n . Theorem R m × n is a real linear space of dimension mn. Basis Example Find a basis for R 3 × 2 . Exercise • Consider A = a 11 a 12 a 21 a 22 and tr ( A ) = a 11 + a 22 . Show that the trace function is a linear function. Matrix-Matrix Multiplication...
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This note was uploaded on 03/31/2010 for the course AMATH 352 taught by Professor Leveque during the Winter '07 term at University of Washington.

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Slides_2010_01_22 - Applied linear algebra and numerical...

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