# How to find eigenvalue of a matrix (attached) having three variables?

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Ismaeel on 18 Jun 2019
Commented: Ismaeel on 26 Jul 2019
I have a 33X33 matrix with three variables (KA1, KA2, KA3). I want to take its eigenvalues. The eigenvalue should be a function of these three variables. Any idea? Thanks.
A =
[ -0.1754, -0.01261, 0.005666, 0.03756, 0.02875, 0.01006, -0.04169, -0.002683, 0.000833, -0.02971, -0.02183, -0.01673, 0.004094, -0.002681, -0.001413, 0, 0, 0, 0.1116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ -0.2057, -13.31, -0.0657, 0.03443, 13.41, -0.1167, 0.5673, 0.00206, -0.000514, 0.4043, 0.01676, 0.01032, -0.1771, 0.2988, -0.1217, 0, 0, 0, 0, 0.1667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0.1378, -0.09722, -1.388, -0.02306, 0.2217, 1.044, -0.3221, -0.004694, -1.429e-5, -0.2296, -0.03819, 0.0002871, 0.1011, 0.06514, -0.1663, 0, 0, 0, 0, 0, 0.1698, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 10.12, 0.5683, -0.2554, -8.933, -1.296, -0.4534, 1.879, 0.121, -0.03755, 1.339, 0.984, 0.7541, -0.1846, 0.1209, 0.06369, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 1.076, 30.76, 0.3436, -0.1801, -32.16, 0.6101, -2.967, -0.01077, 0.002688, -2.114, -0.08764, -0.05399, 0.9263, -1.563, 0.6364, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 5.039, -3.556, 21.52, -0.8434, 8.11, -27.88, -11.78, -0.1717, -0.0005228, -8.397, -1.397, 0.0105, 3.699, 2.383, -6.082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, -3.226, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ -0.3163, 0.07269, -0.02432, 0.05294, -0.1658, -0.04318, -0.3983, -16.94, -0.01262, -0.2839, -15.62, 0.2534, 0.112, -0.2546, 0.1426, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0.1245, -0.001107, 0.01228, -0.02083, 0.002524, 0.0218, 0.2527, -0.01684, -10.82, 0.1801, -0.137, -8.9, -0.0731, -0.08933, 0.1624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ -0.3569, 0.9731, -0.3902, 0.05974, -2.219, -0.6928, -38.3, -0.03862, 0.02101, -36.0, -0.3142, -0.4219, 2.197, -1.111, -1.086, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ -2.2, 0.5057, -0.1692, 0.3683, -1.153, -0.3004, -2.771, -13.36, -0.08779, -1.975, -17.17, 1.763, 0.7792, -1.771, 0.992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ -1.458, 0.01296, -0.1438, 0.244, -0.02957, -0.2554, -2.961, 0.1973, -5.191, -2.11, 1.605, -8.184, 0.8565, 1.047, -1.903, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ -2.86, -11.95, 4.807, 0.4787, 27.26, 8.535, 86.55, 0.4028, -0.2332, 61.68, 3.277, 4.683, -26.26, 13.27, 12.99, -0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7.974, 0, 0, 0, 0, 0]
[ 3.478, 74.73, 10.82, -0.5822, -170.4, 19.21, -170.5, -4.851, -1.489, -121.5, -39.46, 29.91, 51.65, -95.45, 43.8, 0, -0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29.45, 0, 0, 0, 0]
[ 18.45, -61.83, -61.2, -3.087, 141.0, -108.7, -349.2, 6.465, 5.145, -248.9, 52.59, -103.3, 106.1, 92.13, -198.2, 0, 0, -0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62.62, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3.365, 0, 0, 0, 0, 0, 3.185, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3.947, 0, 0, 0, 0, 0, 3.185, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3.536, 0, 0, 0, 0, 0, 3.185, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5143, 0, 0, -2.857, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5143, 0, 0, -2.857, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5143, 0, 0, -2.857, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[ -5.322*KA1, 0.2824*KA1, -0.1263*KA1, 0.8907*KA1, -0.6439*KA1, -0.2243*KA1, -0.2677*KA1, 0.05718*KA1, -0.01764*KA1, -0.1908*KA1, 0.4652*KA1, 0.3543*KA1, -0.06187*KA1, 0.04441*KA1, 0.01746*KA1, 0, 0, 0, -0.9*KA1, 0, 0, 5.0*KA1, 0, 0, -5.0, 0, 0, 0, 0, 0, 0, 0, 0]
[ -1.192*KA2, 1.977*KA2, -0.2315*KA2, 0.1995*KA2, -4.509*KA2, -0.411*KA2, 0.816*KA2, 0.4063*KA2, -0.02598*KA2, 0.5816*KA2, 3.305*KA2, 0.5217*KA2, -0.2788*KA2, 0.3427*KA2, -0.06391*KA2, 0, 0, 0, 0, -0.9*KA2, 0, 0, 5.0*KA2, 0, 0, -5.0, 0, 0, 0, 0, 0, 0, 0]
[ -1.237*KA3, 0.541*KA3, -0.8733*KA3, 0.207*KA3, -1.234*KA3, -1.55*KA3, 0.8115*KA3, 0.09036*KA3, -0.1336*KA3, 0.5783*KA3, 0.7351*KA3, 2.683*KA3, -0.2786*KA3, -0.01786*KA3, 0.2965*KA3, 0, 0, 0, 0, 0, -0.9*KA3, 0, 0, 5.0*KA3, 0, 0, -5.0, 0, 0, 0, 0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10.0, 0, 0, 10.0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10.0, 0, 0, 10.0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10.0, 0, 0, 10.0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.061, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20.0, 0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.061, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20.0, 0]
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.061, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20.0]

johnson wul on 26 Jul 2019
If your matrix is not symmetric, you should change it into a symmetric one by using the formular:
symmetric_Matrix(i,j) = ur_(matrix(i,j)+ur_matrix(i,j)')/2
After doing this just use eig() function to obtain eigenvalues
Ismaeel on 26 Jul 2019

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