display('This is a test')
This is a test
diary off
'Hello world'
ans =
Hello world
x=[1,2,3]
x =
1 2 3
x=[1;2;3]
x =
1
2
3
x'
ans =
1 2 3
x=[1+i;2;3]
x =
1.0000 + 1.0000i
2.0000 + 0.0000i
3.0000 + 0.0000i
i^2
ans =
-1
x'
ans =
Columns 1 through 2
1.0000 - 1.0000i 2.0000 + 0.0000i
Column 3
3.0000 + 0.0000i
x(2)
ans =
2
x(3)
ans =
3
x(1)
ans =
1.0000 + 1.0000i
1:10
ans =
Columns 1 through 8
1 2 3 4 5 6 7 8
Columns 9 through 10
9 10
1:2:10
ans =
1 3 5 7 9
x(1:2)
ans =
1.0000 + 1.0000i
2.0000 + 0.0000i
x([1,3])
ans =
1.0000 + 1.0000i
3.0000 + 0.0000i
x*x'
ans =
Columns 1 through 2
2.0000 + 0.0000i 2.0000 + 2.0000i
2.0000 - 2.0000i 4.0000 + 0.0000i
3.0000 - 3.0000i 6.0000 + 0.0000i
Column 3
3.0000 + 3.0000i
6.0000 + 0.0000i
9.0000 + 0.0000i
x*x'
ans =
2.0000 + 0.0000i 2.0000 + 2.0000i 3.0000 + 3.0000i
2.0000 - 2.0000i 4.0000 + 0.0000i 6.0000 + 0.0000i
3.0000 - 3.0000i 6.0000 + 0.0000i 9.0000 + 0.0000i
A=[1,2;3,4]
A =
1 2
3 4
A^(-1)
ans =
-2.0000 1.0000
1.5000 -0.5000
A^(-1)*A
ans =
1.0000 0
0.0000 1.0000
A^(-0.5)
ans =
0.1031 - 1.2474i 0.1502 + 0.5706i
0.2253 + 0.8559i 0.3284 - 0.3915i
A^(-i)
ans =
9.6655 +14.4690i -4.4717 - 7.0731i
-6.7075 -10.6097i 2.9580 + 3.8593i
help power
.^ Array power.
Z = X.^Y denotes element-by-element powers. X and Y
must have the same dimensions unless one is a scalar.
A scalar can operate into anything.
C = power(A,B) is called for the syntax 'A .^ B' when A or B is an
object.
See also mpower, nthroot, realpow.
Overloaded methods:
codistributed/power
gpuArray/power
Reference page in Help browser
doc power
doc power
A.^(-1)
ans =
1.0000 0.5000
0.3333 0.2500
A
A =
1 2
3 4
det(A)
ans =
-2
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
b=randn(5,1)
b =
-0.8637
0.0774
-1.2141
-1.1135
-0.0068
x=A\b
x =
-2.0998
-0.5691
1.1474
-1.0105
-2.0245
A*x
ans =
-0.8637
0.0774
-1.2141
-1.1135
-0.0068
A*x -b
ans =
1.0e-15 *
0.1110
0.5690
-0.2220
0.2220
0.5794
A=randn(10,5)
A =
1.5326 0.0859 -1.4023 0.6966 0.1873
-0.7697 -1.4916 -1.4224 0.8351 -0.0825
0.3714 -0.7423 0.4882 -0.2437 -1.9330
-0.2256 -1.0616 -0.1774 0.2157 -0.4390
1.1174 2.3505 -0.1961 -1.1658 -1.7947
-1.0891 -0.6156 1.4193 -1.1480 0.8404
0.0326 0.7481 0.2916 0.1049 -0.8880
0.5525 -0.1924 0.1978 0.7223 0.1001
1.1006 0.8886 1.5877 2.5855 -0.5445
1.5442 -0.7648 -0.8045 -0.6669 0.3035
b=randn(10,1)
b =
-0.6003
0.4900
0.7394
1.7119
-0.1941
-2.1384
-0.8396
1.3546
-1.0722
0.9610
x=A\b
x =
0.1968
-0.5451
-0.3891
-0.0027
-0.4322
A*x -b
ans =
1.3178
0.7584
0.3845
-0.9195
-0.0121
1.3472
0.7083
-1.2631
0.4151
-0.0566
A=randn(5,10)
A =
Columns 1 through 7
0.1240 2.9080 -0.2725 -0.3538 0.0335 0.0229 -0.9792
1.4367 0.8252 1.0984 -0.8236 -1.3337 -0.2620 -1.1564
-1.9609 1.3790 -0.2779 -1.5771 1.1275 -1.7502 -0.5336
-0.1977 -1.0582 0.7015 0.5080 0.3502 -0.2857 -2.0026
-1.2078 -0.4686 -2.0518 0.2820 -0.2991 -0.8314 0.9642
Columns 8 through 10
0.5201 -0.1332 -0.2938
-0.0200 -0.7145 -0.8479
-0.0348 1.3514 -1.1201
-0.7982 -0.2248 2.5260
1.0187 -0.5890 1.6555
b=randn(5,1)
b =
0.3075
-1.2571
-0.8655
-0.1765
0.7914
x=A\b
x =
0.5311
0.4001
0
0
0.6801
0
0.7683
0
0
0.6541
Ax-b
{Undefined function or variable 'Ax'.
}
A*x-b
ans =
1.0e-15 *
0.4996
-0.6661
0.3331
0
0.5551
A=randn(5,5)
A =
-1.3320 0.4517 -1.3617 1.0391 -0.1952
-2.3299 -0.1303 0.4550 -1.1176 -0.2176
-1.4491 0.1837 -0.8487 1.2607 -0.3031
0.3335 -0.4762 -0.3349 0.6601 0.0230
0.3914 0.8620 0.5528 -0.0679 0.0513
A=rand(5,5)
A =
0.8176 0.5328 0.6225 0.2305 0.2277
0.7948 0.3507 0.5870 0.8443 0.4357
0.6443 0.9390 0.2077 0.1948 0.3111
0.3786 0.8759 0.3012 0.2259 0.9234
0.8116 0.5502 0.4709 0.1707 0.4302
[V,D]=eig(A)
V =
Columns 1 through 3
-0.4148 + 0.0000i -0.1182 + 0.0000i 0.4221 - 0.1534i
-0.5149 + 0.0000i -0.6330 + 0.0000i -0.3259 + 0.2650i
-0.4091 + 0.0000i 0.6586 + 0.0000i 0.0590 + 0.3036i
-0.4727 + 0.0000i 0.3843 + 0.0000i -0.5393 + 0.0000i
-0.4148 + 0.0000i 0.0623 + 0.0000i 0.1491 - 0.4617i
Columns 4 through 5
0.4221 + 0.1534i 0.4618 + 0.0000i
-0.3259 - 0.2650i 0.0685 + 0.0000i
0.0590 - 0.3036i -0.8713 + 0.0000i
-0.5393 + 0.0000i 0.1456 + 0.0000i
0.1491 + 0.4617i -0.0412 + 0.0000i
D =
Columns 1 through 3
2.5834 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.6672 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.1707 + 0.2981i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 4 through 5
0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i
0.1707 - 0.2981i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.2254 + 0.0000i
doc eig
help eig
eig Eigenvalues and eigenvectors.
E = eig(X) is a vector containing the eigenvalues of a square
matrix X.
[V,D] = eig(X) produces a diagonal matrix D of eigenvalues and a
full matrix V whose columns are the corresponding eigenvectors so
that X*V = V*D.
[V,D] = eig(X,'nobalance') performs the computation with balancing
disabled, which sometimes gives more accurate results for certain
problems with unusual scaling. If X is symmetric, eig(X,'nobalance')
is ignored since X is already balanced.
E = eig(A,B) is a vector containing the generalized eigenvalues
of square matrices A and B.
[V,D] = eig(A,B) produces a diagonal matrix D of generalized
eigenvalues and a full matrix V whose columns are the
corresponding eigenvectors so that A*V = B*V*D.
eig(A,B,'chol') is the same as eig(A,B) for symmetric A and symmetric
positive definite B. It computes the generalized eigenvalues of A and B
using the Cholesky factorization of B.
eig(A,B,'qz') ignores the symmetry of A and B and uses the QZ algorithm.
In general, the two algorithms return the same result, however using the
QZ algorithm may be more stable for certain problems.
The flag is ignored when A and B are not symmetric.
See also condeig, eigs, ordeig.
Overloaded methods:
codistributed/eig
gpuArray/eig
sym/eig
Reference page in Help browser
doc eig
D
D =
Columns 1 through 3
2.5834 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.6672 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.1707 + 0.2981i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 4 through 5
0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i
0.1707 - 0.2981i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.2254 + 0.0000i
size(D)
ans =
5 5
diag(D)
ans =
2.5834 + 0.0000i
-0.6672 + 0.0000i
0.1707 + 0.2981i
0.1707 - 0.2981i
-0.2254 + 0.0000i
V(:,1)
ans =
-0.4148
-0.5149
-0.4091
-0.4727
-0.4148
A*V(:,1)
ans =
-1.0715
-1.3302
-1.0568
-1.2211
-1.0717
(A*V(:,1))./V(:,1)
ans =
2.5834
2.5834
2.5834
2.5834
2.5834
A*V -V*D
ans =
1.0e-15 *
Columns 1 through 3
0.4441 + 0.0000i -0.5551 + 0.0000i 0.2776 - 0.0139i
-0.4441 + 0.0000i -0.6106 + 0.0000i 0.1110 - 0.1180i
0.0000 + 0.0000i -0.4996 + 0.0000i 0.4996 - 0.2082i
0.0000 + 0.0000i -0.4441 + 0.0000i 0.4302 - 0.2776i
0.0000 + 0.0000i -0.0347 + 0.0000i 0.1110 + 0.1596i
Columns 4 through 5
0.2776 + 0.0139i -0.0555 + 0.0000i
0.1110 + 0.1180i 0.3227 + 0.0000i
0.4996 + 0.2082i 0.4718 + 0.0000i
0.4302 + 0.2776i 0.5967 + 0.0000i
0.1110 - 0.1596i -0.2533 + 0.0000i
A
A =
0.8176 0.5328 0.6225 0.2305 0.2277
0.7948 0.3507 0.5870 0.8443 0.4357
0.6443 0.9390 0.2077 0.1948 0.3111
0.3786 0.8759 0.3012 0.2259 0.9234
0.8116 0.5502 0.4709 0.1707 0.4302
(A+A')/2
ans =
0.8176 0.6638 0.6334 0.3045 0.5196
0.6638 0.3507 0.7630 0.8601 0.4929
0.6334 0.7630 0.2077 0.2480 0.3910
0.3045 0.8601 0.2480 0.2259 0.5470
0.5196 0.4929 0.3910 0.5470 0.4302
[V,D]=eig(A)
V =
Columns 1 through 3
-0.4148 + 0.0000i -0.1182 + 0.0000i 0.4221 - 0.1534i
-0.5149 + 0.0000i -0.6330 + 0.0000i -0.3259 + 0.2650i
-0.4091 + 0.0000i 0.6586 + 0.0000i 0.0590 + 0.3036i
-0.4727 + 0.0000i 0.3843 + 0.0000i -0.5393 + 0.0000i
-0.4148 + 0.0000i 0.0623 + 0.0000i 0.1491 - 0.4617i
Columns 4 through 5
0.4221 + 0.1534i 0.4618 + 0.0000i
-0.3259 - 0.2650i 0.0685 + 0.0000i
0.0590 - 0.3036i -0.8713 + 0.0000i
-0.5393 + 0.0000i 0.1456 + 0.0000i
0.1491 + 0.4617i -0.0412 + 0.0000i
D =
Columns 1 through 3
2.5834 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.6672 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.1707 + 0.2981i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 4 through 5
0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i
0.1707 - 0.2981i 0.0000 + 0.0000i
0.0000 + 0.0000i -0.2254 + 0.0000i
diag(D)
ans =
2.5834 + 0.0000i
-0.6672 + 0.0000i
0.1707 + 0.2981i
0.1707 - 0.2981i
-0.2254 + 0.0000i
A=(A+A')/2
A =
0.8176 0.6638 0.6334 0.3045 0.5196
0.6638 0.3507 0.7630 0.8601 0.4929
0.6334 0.7630 0.2077 0.2480 0.3910
0.3045 0.8601 0.2480 0.2259 0.5470
0.5196 0.4929 0.3910 0.5470 0.4302
A
A =
0.8176 0.6638 0.6334 0.3045 0.5196
0.6638 0.3507 0.7630 0.8601 0.4929
0.6334 0.7630 0.2077 0.2480 0.3910
0.3045 0.8601 0.2480 0.2259 0.5470
0.5196 0.4929 0.3910 0.5470 0.4302
[V,D]=eig(A)
V =
0.0606 -0.4469 0.1852 -0.7078 0.5112
-0.6995 -0.0421 -0.4374 0.2253 0.5166
0.4218 0.6911 -0.3740 -0.2080 0.4017
0.5583 -0.4431 -0.0989 0.5788 0.3837
-0.1319 0.3530 0.7904 0.2645 0.4041
D =
-0.7605 0 0 0 0
0 -0.2077 0 0 0
0 0 0.0257 0 0
0 0 0 0.3492 0
0 0 0 0 2.6255
V*V'
ans =
1.0000 -0.0000 -0.0000 -0.0000 -0.0000
-0.0000 1.0000 -0.0000 -0.0000 0.0000
-0.0000 -0.0000 1.0000 -0.0000 -0.0000
-0.0000 -0.0000 -0.0000 1.0000 0.0000
-0.0000 0.0000 -0.0000 0.0000 1.0000
V*V' -eye(5)
ans =
1.0e-15 *
0.2220 -0.0555 -0.7216 -0.3608 -0.1665
-0.0555 -0.2220 -0.1665 -0.0278 0.1943
-0.7216 -0.1665 0.2220 -0.0833 -0.1110
-0.3608 -0.0278 -0.0833 -0.5551 0.0833
-0.1665 0.1943 -0.1110 0.0833 -0.2220
plot(1:10)
plot(1:10,'.')
plot(1:10,'.)
plot(1:10,'.)
|
{Error: A MATLAB string constant is not terminated properly.
}
x=1:10;
plot(x,1+x.^2)
plot(x,1+x.^2,x,x^3)
{Error using ^
Inputs must be a scalar and a square matrix.
To compute elementwise POWER, use POWER (.^) instead.
}
plot(x,1+x.^2,x,x.^3)
plot(x,-5x.^2,x,x.^3)
plot(x,-5x.^2,x,x.^3)
|
{Error: Unexpected MATLAB expression.
}
plot(x,-5+x.^2,x,x.^3)
pwd
ans =
\\nask.man.ac.uk\home$\MATLAB
cd ..
cd MATLAB
pwd
ans =
\\nask.man.ac.uk\home$\MATLAB
exit