type startup.m display('Starting diary') diary(['P:/public_html/PSBC/',date(),'.txt']) cd P:/public_html/PSBC/ A=rand(5,5) A = 0.8147 0.0975 0.1576 0.1419 0.6557 0.9058 0.2785 0.9706 0.4218 0.0357 0.1270 0.5469 0.9572 0.9157 0.8491 0.9134 0.9575 0.4854 0.7922 0.9340 0.6324 0.9649 0.8003 0.9595 0.6787 A=randn(5,5) A = 1.0347 0.8884 1.4384 -0.1022 -0.0301 0.7269 -1.1471 0.3252 -0.2414 -0.1649 -0.3034 -1.0689 -0.7549 0.3192 0.6277 0.2939 -0.8095 1.3703 0.3129 1.0933 -0.7873 -2.9443 -1.7115 -0.8649 1.1093 A=(A+A')/2 A = 1.0347 0.8076 0.5675 0.0958 -0.4087 0.8076 -1.1471 -0.3718 -0.5255 -1.5546 0.5675 -0.3718 -0.7549 0.8448 -0.5419 0.0958 -0.5255 0.8448 0.3129 0.1142 -0.4087 -1.5546 -0.5419 0.1142 1.1093 A=randn(5,5) A = -0.8637 1.5326 -1.0891 0.0859 -0.6156 0.0774 -0.7697 0.0326 -1.4916 0.7481 -1.2141 0.3714 0.5525 -0.7423 -0.1924 -1.1135 -0.2256 1.1006 -1.0616 0.8886 -0.0068 1.1174 1.5442 2.3505 -0.7648 A=(A+A')/2 A = -0.8637 0.8050 -1.1516 -0.5138 -0.3112 0.8050 -0.7697 0.2020 -0.8586 0.9327 -1.1516 0.2020 0.5525 0.1792 0.6759 -0.5138 -0.8586 0.1792 -1.0616 1.6195 -0.3112 0.9327 0.6759 1.6195 -0.7648 A=rand(5,5) A = 0.1966 0.8308 0.7572 0.0540 0.5688 0.2511 0.5853 0.7537 0.5308 0.4694 0.6160 0.5497 0.3804 0.7792 0.0119 0.4733 0.9172 0.5678 0.9340 0.3371 0.3517 0.2858 0.0759 0.1299 0.1622 A=(A+A')/2 A = 0.1966 0.5410 0.6866 0.2636 0.4602 0.5410 0.5853 0.6517 0.7240 0.3776 0.6866 0.6517 0.3804 0.6735 0.0439 0.2636 0.7240 0.6735 0.9340 0.2335 0.4602 0.3776 0.0439 0.2335 0.1622 A*A' ans = 1.0841 1.2351 0.9465 1.2596 0.4611 1.2351 1.7267 1.5050 1.7697 0.7289 0.9465 1.5050 1.4965 1.5484 0.7432 1.2596 1.7697 1.5484 1.9742 0.6802 0.4611 0.7289 0.7432 0.6802 0.4372 A'*A ans = 1.0841 1.2351 0.9465 1.2596 0.4611 1.2351 1.7267 1.5050 1.7697 0.7289 0.9465 1.5050 1.4965 1.5484 0.7432 1.2596 1.7697 1.5484 1.9742 0.6802 0.4611 0.7289 0.7432 0.6802 0.4372 eig(A) ans = -0.6144 -0.1586 0.1340 0.4240 2.4735 A A = 0.1966 0.5410 0.6866 0.2636 0.4602 0.5410 0.5853 0.6517 0.7240 0.3776 0.6866 0.6517 0.3804 0.6735 0.0439 0.2636 0.7240 0.6735 0.9340 0.2335 0.4602 0.3776 0.0439 0.2335 0.1622 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.4885 -0.0143 0.5984 0.9370 2.6406 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.7042 -0.1511 0.0724 0.4092 2.0090 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.7944 -0.3392 -0.1379 0.5537 2.3002 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.3268 0.0097 0.1884 0.6530 2.7409 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.6315 -0.3159 0.3034 0.6032 2.6155 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.1052 0.1364 0.3866 0.6763 2.2638 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.5023 -0.0233 0.4719 0.7411 2.6760 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.5815 -0.2045 0.2057 0.6553 2.6710 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.3552 -0.1394 0.0244 0.5825 2.5685 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.7262 -0.3162 -0.0817 0.2343 2.4924 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.7671 -0.1516 0.1994 0.7026 2.4911 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.5757 -0.1497 0.4879 0.6691 2.3763 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.6371 -0.2100 0.0104 0.3541 2.3223 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.3886 -0.0999 0.1457 0.6215 2.7546 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.6335 -0.2332 0.4642 0.7358 2.0989 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.2172 -0.0650 0.2311 0.3869 2.8350 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.3354 -0.2904 0.0037 0.7281 2.6369 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.5608 0.1401 0.2466 0.6406 2.5139 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.3679 -0.1980 -0.0597 0.2045 2.6807 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.1212 0.1368 0.5627 0.6268 2.4711 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.6054 0.0330 0.3141 0.5608 3.1976 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.6001 0.0746 0.1230 0.6997 2.6458 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.4133 -0.1598 0.0810 0.7062 2.1749 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.9415 -0.3540 0.2878 0.7755 2.6984 A=rand(5,5);A=(A+A')/2;eig(A) ans = -0.3505 -0.1689 0.0074 0.4882 2.4841 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6555 -0.3413 0.2141 0.6087 2.1605 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.8312 -0.2855 0.1220 0.4988 2.2412 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4949 -0.3979 0.3954 0.5259 2.6206 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6351 -0.2829 0.2876 0.6442 2.5464 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.3899 -0.1043 0.2340 0.6357 2.2743 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4552 -0.0970 0.2292 0.6988 2.2252 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.2576 0.2006 0.3848 0.6165 2.1274 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.2759 0.0871 0.2254 0.7001 2.3668 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.7387 -0.2970 0.2364 0.3302 2.4032 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4683 -0.1310 0.1669 0.5509 2.7899 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6261 -0.4786 0.0802 0.4877 2.9233 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5959 -0.3211 0.2472 0.6617 2.3165 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.2312 0.0386 0.5627 0.8287 2.8041 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.7680 -0.2447 0.2377 0.5316 2.8842 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4990 -0.1897 0.4313 0.5338 2.6755 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4502 -0.0464 0.3857 0.9539 2.5369 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6864 -0.3708 0.0245 0.4473 2.6135 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.3557 -0.0166 0.2080 0.6927 3.0551 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6763 -0.0195 0.0958 0.9092 2.4490 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6178 -0.2056 0.3515 0.5448 2.3935 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.7038 -0.2769 0.0425 0.6618 2.5731 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6055 -0.5209 -0.1707 0.2256 2.7348 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5621 -0.0560 0.0635 0.5970 3.1384 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4036 0.0941 0.2500 0.3941 3.2732 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5221 -0.1949 0.2207 0.5416 2.7472 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.3617 0.0636 0.1331 0.4178 2.1566 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6770 -0.1408 0.0473 0.4088 2.9631 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.1892 0.1395 0.1867 0.3336 2.8267 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4584 -0.2033 0.1657 0.4949 2.2913 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5259 -0.2196 0.0340 0.7975 2.6416 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.7962 -0.3787 -0.1732 0.0822 2.5686 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5416 -0.2780 -0.1178 0.4963 1.7037 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.8666 -0.4212 0.2478 0.3596 2.4347 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5042 -0.1711 0.1554 0.8980 2.4978 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5597 -0.1036 0.3102 0.5240 2.2614 A=rand(5,5);A=(A+A')/2;eig(A)' ans = 0.0323 0.0833 0.3479 0.8506 2.6650 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5201 0.0358 0.4739 0.7315 2.0598 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.8424 -0.7607 -0.1125 0.5220 2.8026 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6028 -0.0894 0.1982 0.3876 2.7160 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6296 -0.3372 0.1619 0.4759 2.3503 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6490 -0.4680 -0.1349 0.3564 2.9209 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.7775 -0.3150 0.1468 0.6459 2.8656 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6262 -0.3997 -0.0798 0.4896 2.5329 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5731 -0.2205 0.3128 0.5123 3.0568 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4901 -0.3579 0.3774 0.4742 1.6786 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6615 -0.4100 0.1636 0.5973 3.0103 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6862 -0.2913 -0.0483 0.1534 2.4842 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.3062 0.1093 0.2951 0.7666 3.0911 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5029 -0.1246 0.0974 0.4915 2.1312 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6617 -0.3291 0.0156 0.7641 2.8154 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6028 -0.2167 -0.0301 0.7682 2.7525 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4082 0.2013 0.5646 0.7879 2.4503 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0071 0.0703 0.4188 0.8726 8.0581 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0023 0.1061 0.3326 0.6173 8.9851 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0210 0.1526 0.6398 0.8572 8.6863 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0318 0.1464 0.5508 0.7927 9.8147 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0038 0.2303 0.5837 0.9305 5.2490 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0013 0.1553 0.1724 0.5139 6.6037 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0466 0.1325 0.4300 1.3133 6.1741 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0007 0.1097 0.3630 0.4528 9.0900 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0001 0.0332 0.1790 0.6672 7.1653 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0582 0.1382 0.3466 0.7806 8.3927 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0202 0.0848 0.5463 0.9569 4.1102 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0141 0.1227 0.2499 0.3690 8.9849 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0093 0.0252 0.6288 0.7299 7.5353 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0043 0.1978 0.3423 0.8849 4.3259 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0002 0.2297 0.3064 0.7290 6.9598 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0962 0.1246 0.3271 0.6767 7.3074 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0016 0.1820 0.3708 0.9100 6.5740 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0043 0.1542 0.4285 0.6893 5.6545 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0196 0.1180 0.1805 0.4757 7.9232 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0079 0.1202 0.4675 0.7371 6.8979 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0141 0.0593 0.3351 0.7052 7.1188 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0254 0.3212 0.3838 0.6551 7.8370 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0028 0.0806 0.1064 2.1974 5.9537 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0151 0.1307 0.5787 0.9906 8.8775 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4405 0.2299 0.4761 0.5318 2.1919 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5261 -0.2050 0.3990 0.5830 2.7285 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.6344 -0.1033 0.2295 0.7903 2.9904 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5838 -0.2637 0.1584 0.6093 2.6869 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.5176 -0.1378 0.1065 0.3225 2.3960 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.7357 -0.1709 0.0662 0.5105 2.4992 A=rand(5,5);A=(A+A')/2;eig(A)' ans = -0.4417 -0.1134 0.0099 0.7054 2.6297 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0011 0.0348 0.2671 1.3084 7.6271 A=rand(5,5);A=(A*A');eig(A)' ans = 0.0520 0.1954 0.4470 0.8546 10.4588 edit makemat.m which makemat P:\public_html\PSBC\makemat.m help makemat A = makemat(th,l1,l2) Give the angle th that one eigenvector makes with x axis and two eigenvalues l1,l2 creat a 2x2 symmetric matrix. makemat(0,1,1) ans = 1 0 0 1 makemat(0,2,4) ans = 2 0 0 4 makemat(pi/2,1,1) ans = 1 0 0 1 makemat(pi/4,1,1) ans = 1 0 0 1 makemat(1356489537854875,1,1) ans = 1 0 0 1 makemat(pi/2,1,-1) ans = -1.0000 0.0000 0.0000 1.0000 makemat(6.7,5,8) ans = 5.4917 -1.1106 -1.1106 7.5083 A=makemat(6.7,5,8) A = 5.4917 -1.1106 -1.1106 7.5083 eig(A) ans = 5 8 [V,D]=eig(A) V = -0.9144 0.4048 -0.4048 -0.9144 D = 5 0 0 8 atan(V(2,1)/V(1,1)) ans = 0.4168 cos(6.7) ans = 0.9144 sin(6.7) ans = 0.4048 edit whatconic.m whatconic(A) ans = ellipse whatconic(makemat(0.877.1.-1)) whatconic(makemat(0.877.1.-1)) | {Error: Unexpected MATLAB expression. } whatconic(makemat(0.877,1,-1)) ans = hyperbola whatconic(makemat(0.877,1,0)) ans = degenerate edit myfn myfn(1) ans = 1 x=linspace(-3,3);plot(x,myfn(x)) {Warning: Imaginary parts of complex X and/or Y arguments ignored} x=linspace(0,3);plot(x,myfn(x)) x=1 x = 1 x= (x+1)^(2/3) x = 1.5874 x= (x+1)^(2/3) x = 1.8847 x= (x+1)^(2/3) x = 2.0264 x= (x+1)^(2/3) x = 2.0923 x= (x+1)^(2/3) x = 2.1225 x= (x+1)^(2/3) x = 2.1363 x= (x+1)^(2/3) x = 2.1426 x= (x+1)^(2/3) x = 2.1455 x= (x+1)^(2/3) x = 2.1468 x= (x+1)^(2/3) x = 2.1474 x= (x+1)^(2/3) x = 2.1477 x= (x+1)^(2/3) x = 2.1478 x= (x+1)^(2/3) x = 2.1479 x= (x+1)^(2/3) x = 2.1479 x= (x+1)^(2/3) x = 2.1479 x= (x+1)^(2/3) x = 2.1479 x= (x+1)^(2/3) x = 2.1479 x= (x+1)^(2/3) x = 2.1479 myfn(x) ans = 1.0883e-06 doc fzero fzero(@myfn,1) Exiting fzero: aborting search for an interval containing a sign change because complex function value encountered during search. (Function value at -0.28 is 0.72+0.14816i.) Check function or try again with a different starting value. ans = NaN fzero(@myfn,2) ans = 2.1479 diary off