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Kunze Linear Algebra
· Problem 4.2.3
Polynomials
Mathematics — Methods · polynomial-evaluation-diagonal-matrix
Problem
Let
A
A
A
be an
n
×
n
n \times n
n
×
n
diagonal matrix over the field
F
F
F
, i.e., a matrix satisfying
A
i
j
=
0
A_{ij} = 0
A
ij
=
0
for
i
≠
j
i \neq j
i
=
j
. Let
f
f
f
be the polynomial over
F
F
F
defined by
f
=
(
x
−
A
11
)
⋯
(
x
−
A
n
n
)
.
f = (x - A_{11}) \cdots (x - A_{nn}).
f
=
(
x
−
A
11
)
⋯
(
x
−
A
nn
)
.
What is the matrix
f
(
A
)
f(A)
f
(
A
)
?
Related theory
S Matrix And T Matrix
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