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Kunze Linear Algebra
· Problem 2.3.8
Vector Spaces
Mathematics — Methods · idempotent-basis
Problem
Again let
V
V
V
be the space of
2
×
2
2 \times 2
2
×
2
matrices over
F
F
F
. Find a basis
{
A
1
,
A
2
,
A
3
,
A
4
}
\{A_1, A_2, A_3, A_4\}
{
A
1
,
A
2
,
A
3
,
A
4
}
for
V
V
V
such that
A
j
2
=
A
j
A_j^2 = A_j
A
j
2
=
A
j
for each
j
j
j
.
Related theory
Change Of Basis And The Change Of Basis Matrix
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