Let??™s consider the following relationship:
Inner product or dot product is given as
Outer product is given as
The inner and outer products are related as follows:
x* # y Trace (x # y*)
A x # y*
k x* # y
Trace [UAU*] Trace [A] if U unitary matrix
Trace [ABC] Trace [BCA] Trace [CAB]
Trace [A B] Trace [A] Trace [B]
det cA C
B Dd det(A) # det(D CA1B)
C1 > B1 B1AB1 B1(I AB1)
C1 (B A)1 (I B1A)1B1 >(I B1A)B1
A B C
(AB)1 B1A1
(AB)T BTAT
Z A1 Z
1
Z AZ
Z AZ Z BZ Z ABZ
Z AT Z Z AZ
Z kAZ kn Z AZ
[A] Z AZ
525
Given a square matrix, A, we can write down the following relationships with eigenvalue and
eigenvector.
For Hermitian matrices, we provide the mathematical relationship between the arithmetic mean and
the geometric mean.
A square Hermitian matrix can be diagonalized as
where D diagonal matrix, , and U is a unitary matrix, or .
We can define a Rayleigh quotient as
The Frobenius or Euclidean norm is given as
iAiF a aM1
i0
lib1/2
R(x)
x* # A # x
x* # x
U* U1 U* # U I 5l0, l1,c, lM16 A U # D # U*
1
M
# Trace [A] [det [A]]1/M
1
M
# aM1
i0
li cqM1
i0
li d1/M
det [A] qM1
i0
li
Trace [A] aM1
i0
li
A # v l # v
v
l
526 APPENDIX F
INDEX
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2G cellular systems, digital modulation
schemes used by, 1
2G IS-95 CDMA
downlink spreading example, 349??“351
uplink spreading example, 351??“353
3G terminal UE statistics
canonical/classical UE architecture,
496??“499
overview, 495??“496
3G wideband CDMA
3GPP feasibility study of OFDM, 484??“489
OFDM reception, 480??“484
OFDM transmission, 479??“480
overview, 343??“345, 477??“479
4G system, development of, 1
16-QAM bit error rate in AWGN channel,
511??“512
64-QAM formula, 512
256-QAM formula, 512
AAA (adaptive antenna arrays), 452??“453.
Pages:
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844