12-functionspace

12-functionspace - FUNCTION SPACES/LINEAR MAPS, Math 21b,...

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Unformatted text preview: FUNCTION SPACES/LINEAR MAPS, Math 21b, O. Knill Homework: Section 4.1 6-11,36,48,58,44*,12*-15* FROM VECTORS TO FUNCTIONS. Vectors can be displayed in different ways: 1 2 5 3 2 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 The values ( i, ~v i ) can be interpreted as the graph of a function f : 1 , 2 , 3 , 4 , 5 , 6 R , where f ( i ) = ~v i . LINEAR SPACES. A space X in which we can add, scalar multiplications and where basic laws like commutativity, distributivity and associativity hold is called a linear space . Examples: Lines, planes and more generally, the n-dimensional Euclidean space. P n , the space of all polynomials of degree n . The space P of all polynomials. C , the space of all smooth functions on the line C , the space of all continuous functions on the line. C 1 , the space of all differentiable functions on the line....
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This note was uploaded on 04/06/2008 for the course MATH 21B taught by Professor Judson during the Spring '03 term at Harvard.

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