Page 149 - DMTH502_LINEAR_ALGEBRA

Unit 10: Linear Functionals

Notes
( f ) 1, ( ) 1, ( ) 3
f
f
1 2 3
c
a
b
and if ( , , ), find f( ).
3
)
2. Let ( 1 , 2 , 3 be the basis for C defined by
(1, 0, 1), (1, 1, 1), (2, 2, 0).
1 2 3
Find the dual basis of .
Answers: Self Assessment
)
1. The dimension of W* is 2 and the basis ( f 1 , f 2 for W* is given by
f (x x , ... ) 4x 3x 2x x
x
,
1 1 2 5 1 2 3 4
x
,
f 2 (x x 2 , ... ) 5x 1 2x 2 x 3 x 5
5
1
)
2. The dimension of W* is 2 and the basis ( f 1 , f 2 for W* is given by
,
,
,
f 1 (x x x x x 5 ) 2x 1 x 2
,
4
1
3
2
,
f 2 (x x x x x 5 ) 3x 1 4x 3 x 4
,
,
,
1
2
4
3
10.6 Further Readings
Books Ervin Kreyszig, Introductory Functional Analysis with Applications
Kenneth Hoffman and Ray Kunze, Linear Algebra

LOVELY PROFESSIONAL UNIVERSITY 143