necessarily normal and thus may not have a spectral decomposition. However, they have a related DE Mn(R) UE Mn(C) Hermitian A* = A Real symmetric DE Mn(R) AT = A U E Mn(R) decomposition that is presented in Exercise 2.3.26. Table 2.1: A summary of which parts of complex for different types of matrices Exercises solu 2.1.4 F 2.1.1 For each of the following matrices, say whether it is (i) unitary, (ii) Hermitian, (iii) skew-Hermitian, (iv) normal. It may have multiple properties or even none of the listed properties. ng norm *(a) 1. 3. 4 2. (в) * b) 2. -2 2 1. 1. 2i (p) 1. (a) * (a) * (e) 1+ (F) 0. (8) 0. 1. -1 2i 2.1.5 I 0. true and 2.1.2 Determine which of the following matrices are nor- (a) If mal. * (b) If (b) 1 1 1 (в) * -1 * (d) TI (e) If 1. 3. 1.
necessarily normal and thus may not have a spectral decomposition. However, they have a related DE Mn(R) UE Mn(C) Hermitian A* = A Real symmetric DE Mn(R) AT = A U E Mn(R) decomposition that is presented in Exercise 2.3.26. Table 2.1: A summary of which parts of complex for different types of matrices Exercises solu 2.1.4 F 2.1.1 For each of the following matrices, say whether it is (i) unitary, (ii) Hermitian, (iii) skew-Hermitian, (iv) normal. It may have multiple properties or even none of the listed properties. ng norm *(a) 1. 3. 4 2. (в) * b) 2. -2 2 1. 1. 2i (p) 1. (a) * (a) * (e) 1+ (F) 0. (8) 0. 1. -1 2i 2.1.5 I 0. true and 2.1.2 Determine which of the following matrices are nor- (a) If mal. * (b) If (b) 1 1 1 (в) * -1 * (d) TI (e) If 1. 3. 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:necessarily normal
and thus may not
have a spectral
decomposition.
However, they
have a related
DE Mn(R)
UE Mn(C)
Hermitian
A* = A
Real symmetric DE Mn(R)
AT = A
U E Mn(R)
decomposition that
is presented in
Exercise 2.3.26.
Table 2.1: A summary of which parts of
complex for different types of matrices
Exercises
solu
2.1.4 F
2.1.1 For each of the following matrices, say whether it is
(i) unitary, (ii) Hermitian, (iii) skew-Hermitian, (iv) normal.
It may have multiple properties or even none of the listed
properties.
ng norm
*(a)
1.
3.
4
2.
(в) *
b)
2.
-2 2
1.
1.
2i
(p)
1.
(a) *
(a) *
(e)
1+
(F)
0.
(8)
0.
1.
-1 2i
2.1.5 I
0.
true and
2.1.2 Determine which of the following matrices are nor-
(a) If
mal.
* (b) If
(b)
1
1 1
(в) *
-1
* (d) TI
(e) If
1.
3.
1.
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