什么是对称反循环矩阵?对称反循环矩阵的次对角线一定都是0

Question

什么是对称反循环矩阵?对称反循环矩阵的次对角线一定都是0

Answer 1

可以使用det(行列式的值),inv(可逆矩阵的逆),pinv(不可逆矩阵的逆,即伪逆),eig(特征值与特征向量);
a=magic(6),det(a),inv(a),pinv(a),[v,d]=eig(a)
a =
35 1 6 26 19 24
3 32 7 21 23 25
31 9 2 22 27 20
8 28 33 17 10 15
30 5 34 12 14 16
4 36 29 13 18 11
ans =
-8.0495e-009
Warning:Matrix is close to singular or badly scaled.
Results may be inaccurate.RCOND = 5.601125e-018.
ans =
1.0e+014 *
-3.2169 -0.0000 3.2169 3.2169 -0.0000 -3.2169
-3.2169 -0.0000 3.2169 3.2169 -0.0000 -3.2169
1.6084 0.0000 -1.6084 -1.6084 0.0000 1.6084
3.2169 0.0000 -3.2169 -3.2169 0.0000 3.2169
3.2169 0.0000 -3.2169 -3.2169 0.0000 3.2169
-1.6084 0.0000 1.6084 1.6084 0.0000 -1.6084
ans =
0.0115 -0.0386 0.0254 0.0054 -0.0139 0.0192
0.0023 -0.0201 0.0162 0.0146 -0.0324 0.0285
-0.0081 0.0030 -0.0151 0.0042 0.0277 -0.0027
0.0540 -0.0417 -0.0016 0.0601 -0.0664 0.0046
-0.0409 0.0231 0.0285 -0.0533 0.0355 0.0162
-0.0097 0.0833 -0.0444 -0.0220 0.0586 -0.0568
v =
0.4082 -0.2887 0.4082 0.1507 0.4714 -0.4769
0.4082 0.5774 0.4082 0.4110 0.4714 -0.4937
0.4082 -0.2887 0.4082 -0.2602 -0.2357 0.0864
0.4082 0.2887 -0.4082 0.4279 -0.4714 0.1435
0.4082 -0.5774 -0.4082 -0.7465 -0.4714 0.0338
0.4082 0.2887 -0.4082 0.0171 0.2357 0.7068
d =
111.0000 0 0 0 0 0
0 27.0000 0 0 0 0
0 0 -27.0000 0 0 0
0 0 0 9.7980 0 0
0 0 0 0 -0.0000 0
0 0 0 0 0 -9.7980