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Kunze Linear Algebra
· Problem 4.2.1
Polynomials
Mathematics — Methods · polynomial-evaluation-matrix
Problem
Let
F
F
F
be a subfield of the complex numbers and let
A
A
A
be the following
2
×
2
2 \times 2
2
×
2
matrix over
F
F
F
A
=
[
2
1
−
1
3
]
.
A = \begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix}.
A
=
[
2
−
1
1
3
]
.
For each of the following polynomials
f
f
f
over
F
F
F
, compute
f
(
A
)
f(A)
f
(
A
)
. ((a))
f
=
x
2
−
x
+
2
f = x^2 - x + 2
f
=
x
2
−
x
+
2
; ((b))
f
=
x
3
−
1
f = x^3 - 1
f
=
x
3
−
1
; ((c))
f
=
x
2
−
5
x
+
7
f = x^2 - 5x + 7
f
=
x
2
−
5
x
+
7
.
Related theory
S Matrix And T Matrix
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