Question

In: Electrical Engineering

Generate 8 × 8 random complex unitary matrix in Matlab. You can only use eig and...

Generate 8 × 8 random complex unitary matrix in Matlab. You can only use eig and randn Matlab functions. Your code can only have two lines and no semicolumns. You should generate a different random unitary matrix with each run.

Solutions

Expert Solution

MATLAB CODE

x=(randn(8)+1i*randn(8))
[X,Y]=eigs(x)

% Randn(x) willl generate 8 X 8 random matrix
% [a,b] = eigs(___) returns diagonal matrix Y containing the eigenvalues on the main diagonal,
% and matrix A whose columns are the corresponding eigenvectors

RESULTS

RUN 1

x =

Columns 1 through 4

-1.5579 + 0.7667i -1.6439 - 1.1114i -0.8407 + 0.9295i 1.3067 + 0.7609i
-2.0666 + 1.5235i 1.5815 + 0.4682i -0.3495 - 0.0904i -0.2844 + 0.2379i
-0.0726 + 0.5768i 0.2926 + 0.3226i 0.0296 - 2.6411i -0.7917 - 0.2084i
0.7591 + 0.4260i -1.1876 + 0.1000i 1.9524 - 0.4861i 0.2406 + 0.0247i
-0.0817 - 0.0429i 1.0759 + 0.3014i 0.4590 + 0.1960i -0.0946 - 0.0281i
-0.1585 - 1.2423i -1.2974 + 0.0238i -0.3993 + 0.9597i 0.7932 + 0.1404i
0.0065 - 0.5050i -0.1218 - 0.0221i -0.2254 + 1.3803i 0.9594 + 0.2376i
-1.0646 + 0.3259i 0.7408 - 0.0088i -0.2803 - 0.9415i 1.0871 - 0.6715i

Columns 5 through 8

0.6472 - 1.0450i -0.2993 - 1.0290i -1.6488 - 0.2256i -0.4667 - 0.6127i
0.6326 + 0.9658i -1.7210 + 0.2065i -0.1820 - 0.9660i -1.4358 + 2.0718i
1.9033 - 0.2198i 0.1834 + 1.3411i 0.6157 + 0.0950i -0.9777 + 0.6370i
-1.1600 + 1.4145i -0.2597 + 1.3327i -0.3767 - 0.2567i 0.6059 + 0.0749i
-0.3473 - 0.9242i -1.3548 - 1.2849i -0.6980 + 2.3101i -0.1137 + 1.1233i
-1.6951 - 0.5941i -1.1574 + 1.6184i 0.3041 + 0.1901i 0.7646 - 0.0331i
0.9194 + 1.4213i -0.7620 + 0.6616i 1.1011 - 0.1734i 0.6699 - 0.0977i
0.0215 + 1.4076i -0.2503 + 0.2273i -0.4466 - 0.0140i 0.3758 - 0.5566i

>> xy

x =

Columns 1 through 4

0.2200 + 0.5013i -1.1064 + 0.1095i 0.8198 - 0.9035i 0.1489 - 0.3237i
-1.7114 - 0.3238i 1.7906 - 1.5513i 0.0555 - 0.4959i 1.5319 - 0.9805i
-1.2058 + 0.5542i 2.1624 - 0.3551i -0.3531 + 0.3745i 0.5318 + 1.1796i
-1.7729 + 0.6424i -0.8193 + 1.3986i 1.6931 - 2.3705i -0.7597 + 0.8946i
-0.0725 + 0.1826i -0.0370 - 0.5135i 0.7111 + 0.6151i 0.3480 - 0.1429i
-1.7211 - 2.0275i 1.9630 + 1.9172i -0.6328 + 0.2795i -0.6978 - 0.5935i
0.7019 + 1.0231i -0.5403 + 0.7784i 0.3927 + 0.8189i 2.0193 + 0.2489i
-1.0055 - 3.4915i 1.7175 - 0.2465i -0.8780 + 2.0475i -1.7937 - 1.1298i

Columns 5 through 8

-0.6595 + 0.0661i -0.4717 - 1.0462i 0.9842 - 0.5474i 0.9248 - 1.3187i
0.7715 - 0.6379i -0.1142 + 0.6187i 0.9931 - 1.6510i 1.4470 - 0.4741i
-0.8203 - 0.8193i 0.3695 + 1.3050i 0.6682 + 0.8928i 0.5958 + 0.9874i
0.0179 + 0.9680i -0.6186 + 1.0235i -0.0650 - 0.5071i 2.0533 - 2.0730i
0.6545 + 0.0303i 0.8001 - 2.1154i -0.6201 - 0.3298i -1.5293 + 1.2440i
1.2577 + 1.3511i 0.4267 + 0.6817i 0.2241 + 0.1684i 0.0227 - 0.3152i
-0.9271 - 1.0864i -0.4723 + 0.0087i -0.4661 + 2.5367i 0.0953 + 1.3993i
-0.1699 + 0.2403i 0.2760 + 0.3343i -0.3321 + 2.2936i 1.6145 - 0.8799i


X =

Columns 1 through 4

-0.0970 + 0.0723i 0.1069 + 0.3899i 0.2483 + 0.0068i -0.1139 + 0.0617i
-0.0300 - 0.3435i 0.0391 + 0.0477i -0.2607 + 0.1065i -0.2313 + 0.6020i
0.2150 - 0.3870i -0.2858 - 0.0100i -0.0774 - 0.1616i -0.1924 + 0.3390i
-0.1690 - 0.0473i -0.2856 + 0.4024i -0.1595 - 0.2423i 0.0795 + 0.0911i
0.3006 + 0.1640i -0.0078 - 0.0357i -0.2191 + 0.4353i -0.3026 - 0.2437i
-0.0447 + 0.3153i -0.0932 - 0.3303i -0.6309 - 0.0243i -0.1752 - 0.4379i
0.1615 - 0.1286i -0.0562 + 0.2718i 0.2594 - 0.1030i -0.0931 - 0.0798i
-0.4733 + 0.3928i -0.3715 - 0.4162i -0.0154 + 0.1689i -0.1068 - 0.0314i

Columns 5 through 6

-0.0997 + 0.0125i -0.1404 - 0.2363i
-0.2298 + 0.0089i 0.3379 - 0.0680i
-0.1058 + 0.1386i 0.1155 + 0.4059i
-0.4902 + 0.1129i -0.4579 + 0.1455i
0.3664 + 0.0339i -0.1547 - 0.3464i
-0.0980 - 0.2261i -0.3292 + 0.0738i
0.5752 + 0.0716i -0.0201 - 0.2954i
0.1903 - 0.2918i -0.1763 - 0.1423i


Y =

Columns 1 through 4

1.5557 - 3.6093i 0 0 0
0 1.8370 + 4.2710i 0 0
0 0 3.2918 + 0.8581i 0
0 0 0 1.9327 - 1.7584i
0 0 0 0
0 0 0 0

Columns 5 through 6

0 0
0 0
0 0
0 0
-2.1825 + 2.2491i 0
0 -2.2800 - 1.4119i

>>

RUN 2

>> xy

x =

Columns 1 through 4

0.2200 + 0.5013i -1.1064 + 0.1095i 0.8198 - 0.9035i 0.1489 - 0.3237i
-1.7114 - 0.3238i 1.7906 - 1.5513i 0.0555 - 0.4959i 1.5319 - 0.9805i
-1.2058 + 0.5542i 2.1624 - 0.3551i -0.3531 + 0.3745i 0.5318 + 1.1796i
-1.7729 + 0.6424i -0.8193 + 1.3986i 1.6931 - 2.3705i -0.7597 + 0.8946i
-0.0725 + 0.1826i -0.0370 - 0.5135i 0.7111 + 0.6151i 0.3480 - 0.1429i
-1.7211 - 2.0275i 1.9630 + 1.9172i -0.6328 + 0.2795i -0.6978 - 0.5935i
0.7019 + 1.0231i -0.5403 + 0.7784i 0.3927 + 0.8189i 2.0193 + 0.2489i
-1.0055 - 3.4915i 1.7175 - 0.2465i -0.8780 + 2.0475i -1.7937 - 1.1298i

Columns 5 through 8

-0.6595 + 0.0661i -0.4717 - 1.0462i 0.9842 - 0.5474i 0.9248 - 1.3187i
0.7715 - 0.6379i -0.1142 + 0.6187i 0.9931 - 1.6510i 1.4470 - 0.4741i
-0.8203 - 0.8193i 0.3695 + 1.3050i 0.6682 + 0.8928i 0.5958 + 0.9874i
0.0179 + 0.9680i -0.6186 + 1.0235i -0.0650 - 0.5071i 2.0533 - 2.0730i
0.6545 + 0.0303i 0.8001 - 2.1154i -0.6201 - 0.3298i -1.5293 + 1.2440i
1.2577 + 1.3511i 0.4267 + 0.6817i 0.2241 + 0.1684i 0.0227 - 0.3152i
-0.9271 - 1.0864i -0.4723 + 0.0087i -0.4661 + 2.5367i 0.0953 + 1.3993i
-0.1699 + 0.2403i 0.2760 + 0.3343i -0.3321 + 2.2936i 1.6145 - 0.8799i


X =

Columns 1 through 4

-0.0970 + 0.0723i 0.1069 + 0.3899i 0.2483 + 0.0068i -0.1139 + 0.0617i
-0.0300 - 0.3435i 0.0391 + 0.0477i -0.2607 + 0.1065i -0.2313 + 0.6020i
0.2150 - 0.3870i -0.2858 - 0.0100i -0.0774 - 0.1616i -0.1924 + 0.3390i
-0.1690 - 0.0473i -0.2856 + 0.4024i -0.1595 - 0.2423i 0.0795 + 0.0911i
0.3006 + 0.1640i -0.0078 - 0.0357i -0.2191 + 0.4353i -0.3026 - 0.2437i
-0.0447 + 0.3153i -0.0932 - 0.3303i -0.6309 - 0.0243i -0.1752 - 0.4379i
0.1615 - 0.1286i -0.0562 + 0.2718i 0.2594 - 0.1030i -0.0931 - 0.0798i
-0.4733 + 0.3928i -0.3715 - 0.4162i -0.0154 + 0.1689i -0.1068 - 0.0314i

Columns 5 through 6

-0.0997 + 0.0125i -0.1404 - 0.2363i
-0.2298 + 0.0089i 0.3379 - 0.0680i
-0.1058 + 0.1386i 0.1155 + 0.4059i
-0.4902 + 0.1129i -0.4579 + 0.1455i
0.3664 + 0.0339i -0.1547 - 0.3464i
-0.0980 - 0.2261i -0.3292 + 0.0738i
0.5752 + 0.0716i -0.0201 - 0.2954i
0.1903 - 0.2918i -0.1763 - 0.1423i


Y =

Columns 1 through 4

1.5557 - 3.6093i 0 0 0
0 1.8370 + 4.2710i 0 0
0 0 3.2918 + 0.8581i 0
0 0 0 1.9327 - 1.7584i
0 0 0 0
0 0 0 0

Columns 5 through 6

0 0
0 0
0 0
0 0
-2.1825 + 2.2491i 0
0 -2.2800 - 1.4119i

>> xy

x =

Columns 1 through 4

0.1016 - 0.8396i -0.5215 - 0.5704i 1.8258 - 1.5031i 0.3618 - 0.2942i
-0.0179 - 1.6606i 0.1271 + 0.9340i 0.2043 + 0.9218i 0.8537 - 0.5048i
-0.9603 + 3.0125i 2.1130 - 1.1383i -1.1634 + 0.1632i -0.8098 - 1.9270i
1.1728 + 1.5008i 0.5413 + 1.9572i 0.1206 - 0.8147i -1.4671 + 0.5214i
-0.3653 - 0.3590i -0.6551 - 1.7632i -1.4435 + 0.4037i -0.1039 - 2.0544i
-0.4634 - 0.1149i -0.8695 - 0.3233i 0.5823 + 0.7562i -0.8229 - 0.2698i
0.1950 + 0.3589i -0.2389 + 0.8726i -0.1815 + 2.1844i 0.4250 - 0.2750i
-0.0669 - 0.0121i -1.5760 + 0.1179i 0.0420 - 0.0938i -1.8547 + 0.8451i

Columns 5 through 8

0.8586 - 2.7712i -0.8607 + 1.2064i -0.5061 - 1.0578i -1.3479 - 0.5703i
0.3064 + 0.9181i 0.2069 + 0.1973i -0.1843 + 0.1515i 1.5479 - 0.3939i
-1.1116 - 0.5193i -0.2075 - 0.7069i 0.4020 + 0.4113i -0.6166 - 1.0174i
-0.3172 - 1.2930i 0.3403 + 1.2164i 0.5392 + 0.0705i -0.6986 + 0.2502i
0.8379 - 0.0087i -0.4981 + 0.3672i -0.7336 - 1.9330i -1.4236 + 0.2521i
2.4265 + 0.2334i -1.4214 - 1.2675i -0.2684 + 0.8187i -0.1096 - 0.7715i
-0.3511 - 0.4242i -0.2708 + 0.6211i 0.8706 + 1.2618i -0.1027 + 0.9195i
1.3820 - 1.4694i 0.4397 - 1.7955i 0.3308 + 1.1673i -0.3227 + 0.8522i


X =

Columns 1 through 4

0.3540 + 0.2806i -0.0828 + 0.5477i -0.1527 - 0.0982i 0.1790 - 0.3628i
0.0032 + 0.2592i 0.0190 - 0.0142i 0.3871 + 0.0995i -0.3138 + 0.2620i
0.0738 - 0.6403i -0.0246 - 0.3344i 0.0421 + 0.0613i 0.3478 + 0.4473i
0.0724 - 0.4601i -0.0589 - 0.1153i -0.1237 - 0.6318i -0.0464 - 0.1443i
-0.0218 - 0.0959i -0.1498 + 0.3492i 0.2682 + 0.1910i 0.1370 - 0.1690i
-0.0038 + 0.2402i -0.4232 - 0.0033i 0.3787 - 0.1816i 0.0261 + 0.0159i
-0.1262 + 0.0710i 0.0643 + 0.2199i 0.1041 + 0.0158i -0.1558 + 0.4511i
-0.0875 - 0.0187i -0.4313 - 0.0373i -0.2441 - 0.1785i -0.1322 - 0.1783i

Columns 5 through 6

-0.3726 - 0.2707i 0.0662 + 0.2174i
-0.0209 + 0.2478i 0.0858 - 0.4089i
0.0878 - 0.1453i -0.4283 - 0.0469i
-0.1964 - 0.1290i 0.0337 + 0.0604i
0.3122 + 0.1829i -0.1114 - 0.1461i
0.1916 - 0.0059i -0.2345 - 0.0480i
0.3040 + 0.3231i -0.4241 + 0.1025i
0.4119 - 0.3284i 0.0533 + 0.5470i


Y =

Columns 1 through 4

-4.1242 - 2.1950i 0 0 0
0 -0.7566 - 3.1684i 0 0
0 0 -2.4909 + 1.6185i 0
0 0 0 1.9770 + 3.2012i
0 0 0 0
0 0 0 0

Columns 5 through 6

0 0
0 0
0 0
0 0
1.6168 + 1.4220i 0
0 0.3883 + 2.8270i

Manojponduru answered 3 months ago
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