Discrete Mathematical Structures by Pearson

12-34 Discrete Mathematical Structures

The scalars are unique because if we also have



uc

u

ii

i

n

=

=

∑

′

1

then

()ccu

iii

i

n

−=

=

∑

′



0

1

As



u

i

(i = 1, 2,…, n) are linearly independent, c

i

- c

i

′ = 0 for all i, that is c

i

′ = c

i

. We shall call

c

i

, the i th coordinate of



u

relative to ordered basis



…



uu u

n12

,,

,.

{}

If



vd

u

ii

i

n

=

=

∑

1

, then

 

uv cdu

ii

i

i

n

+= +

=

∑

()

1

and c

i

+ d

i

is the i th coordinate of



uv+

relative

to ordered basis



…



uu u

n12

,,

,.

{}

12.7 LINEAR TRANSFORMATION

Linear mappings from one vector space to another have acquired an important role in mathematics.

Each linear transformation can be represented by a matrix, which enables us to work with the

matrix in place of the transformation.

Definition 12.5 Let U and V be vector spaces over the ...