Introduction

Consider tw o finit e sequence s o f vector s i n th e plan e

A =

M

and B

T

0

[2

' V 3

1"

2

2

VI

1

2

2

s

The sequence A i s an orthonormal basi s (ONB ) fo r R 2, an d i t ha s

certain propertie s whic h w e recal l fro m calculu s an d linea r algebra .

The sequenc e B i s a bi t different . Le t u s compar e th e two .

• Bot h A an d B ar e spanning set s for R

2,

s o every x G R

2

ca n

be writte n a s a linea r combinatio n o f th e vector s i n A , an d

similarly fo r th e vector s i n B.

• Th e vectors in A ar e linearly independent , s o the coefficient s

in th e linea r expansio n x — c\

c2

where c* G

1

http://dx.doi.org/10.1090/stml/040/01