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Element pl-matrix-input: Matrix algebra with complex values

Two matrices $A$ and $B$ are given as follows: 

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A = [0.70-0.80j -0.90-0.50j 0.90-0.30j -0.20-0.30j -0.50+0.70j; -0.10+0.60j 0.90+0.60j 0.90-0.10j -0.50+0.20j 0.80-0.30j; 0.30+0.40j -0.50+0.00j -0.10-0.40j -0.50+0.90j -0.50+0.40j];
B = [-0.80+0.30j -0.20+0.60j -0.70+0.00j 0.50+0.20j 0.60+0.70j; -0.10-0.80j 0.30-0.80j 0.50+1.00j 0.20+0.80j 1.00+0.10j; -0.70-0.10j 0.10-1.00j 1.00-0.30j 0.40+0.90j -1.00+0.20j; 0.40-0.20j -0.90+0.70j -0.30-0.50j -0.80-0.80j -0.20-0.40j; -0.40-0.60j -0.80+0.40j -0.20+0.20j 0.60+0.30j 0.00+0.50j];

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A = {{0.70-0.80j, -0.90-0.50j, 0.90-0.30j, -0.20-0.30j, -0.50+0.70j}, {-0.10+0.60j, 0.90+0.60j, 0.90-0.10j, -0.50+0.20j, 0.80-0.30j}, {0.30+0.40j, -0.50+0.00j, -0.10-0.40j, -0.50+0.90j, -0.50+0.40j}};
B = {{-0.80+0.30j, -0.20+0.60j, -0.70+0.00j, 0.50+0.20j, 0.60+0.70j}, {-0.10-0.80j, 0.30-0.80j, 0.50+1.00j, 0.20+0.80j, 1.00+0.10j}, {-0.70-0.10j, 0.10-1.00j, 1.00-0.30j, 0.40+0.90j, -1.00+0.20j}, {0.40-0.20j, -0.90+0.70j, -0.30-0.50j, -0.80-0.80j, -0.20-0.40j}, {-0.40-0.60j, -0.80+0.40j, -0.20+0.20j, 0.60+0.30j, 0.00+0.50j}};

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import numpy as np

A = np.array([[0.70-0.80j, -0.90-0.50j, 0.90-0.30j, -0.20-0.30j, -0.50+0.70j], [-0.10+0.60j, 0.90+0.60j, 0.90-0.10j, -0.50+0.20j, 0.80-0.30j], [0.30+0.40j, -0.50+0.00j, -0.10-0.40j, -0.50+0.90j, -0.50+0.40j]])
B = np.array([[-0.80+0.30j, -0.20+0.60j, -0.70+0.00j, 0.50+0.20j, 0.60+0.70j], [-0.10-0.80j, 0.30-0.80j, 0.50+1.00j, 0.20+0.80j, 1.00+0.10j], [-0.70-0.10j, 0.10-1.00j, 1.00-0.30j, 0.40+0.90j, -1.00+0.20j], [0.40-0.20j, -0.90+0.70j, -0.30-0.50j, -0.80-0.80j, -0.20-0.40j], [-0.40-0.60j, -0.80+0.40j, -0.20+0.20j, 0.60+0.30j, 0.00+0.50j]])

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A = matrix(c(0.70-0.80j, -0.90-0.50j, 0.90-0.30j, -0.20-0.30j, -0.50+0.70j, -0.10+0.60j, 0.90+0.60j, 0.90-0.10j, -0.50+0.20j, 0.80-0.30j, 0.30+0.40j, -0.50+0.00j, -0.10-0.40j, -0.50+0.90j, -0.50+0.40j), nrow = 3, ncol = 5, byrow = TRUE)
B = matrix(c(-0.80+0.30j, -0.20+0.60j, -0.70+0.00j, 0.50+0.20j, 0.60+0.70j, -0.10-0.80j, 0.30-0.80j, 0.50+1.00j, 0.20+0.80j, 1.00+0.10j, -0.70-0.10j, 0.10-1.00j, 1.00-0.30j, 0.40+0.90j, -1.00+0.20j, 0.40-0.20j, -0.90+0.70j, -0.30-0.50j, -0.80-0.80j, -0.20-0.40j, -0.40-0.60j, -0.80+0.40j, -0.20+0.20j, 0.60+0.30j, 0.00+0.50j), nrow = 5, ncol = 5, byrow = TRUE)

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from sympy import *

A = Matrix([[0.70-0.80j, -0.90-0.50j, 0.90-0.30j, -0.20-0.30j, -0.50+0.70j], [-0.10+0.60j, 0.90+0.60j, 0.90-0.10j, -0.50+0.20j, 0.80-0.30j], [0.30+0.40j, -0.50+0.00j, -0.10-0.40j, -0.50+0.90j, -0.50+0.40j]])
B = Matrix([[-0.80+0.30j, -0.20+0.60j, -0.70+0.00j, 0.50+0.20j, 0.60+0.70j], [-0.10-0.80j, 0.30-0.80j, 0.50+1.00j, 0.20+0.80j, 1.00+0.10j], [-0.70-0.10j, 0.10-1.00j, 1.00-0.30j, 0.40+0.90j, -1.00+0.20j], [0.40-0.20j, -0.90+0.70j, -0.30-0.50j, -0.80-0.80j, -0.20-0.40j], [-0.40-0.60j, -0.80+0.40j, -0.20+0.20j, 0.60+0.30j, 0.00+0.50j]])

Find the product of these two matrices:

Correct answer

$AB=$ [-0.81+1.68j -0.03-0.41j 0.24-1.21j 0.77+0.28j -1.14-0.21j; -1.01-1.49j 0.19-1.6j 0.94+0.82j 1.11+2.19j -0.19+1.82j; 0.14+1.06j -0.8-1.12j -0.06-1.35j 0.99-0.62j -0.16+0.55j]

$AB=$ [[-0.81+1.68j, -0.03-0.41j, 0.24-1.21j, 0.77+0.28j, -1.14-0.21j], [-1.01-1.49j, 0.19-1.6j, 0.94+0.82j, 1.11+2.19j, -0.19+1.82j], [0.14+1.06j, -0.8-1.12j, -0.06-1.35j, 0.99-0.62j, -0.16+0.55j]]

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Title:
Element pl-matrix-input: Matrix algebra with complex values

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Started at:
2026-09-19 08:00:25 (CDT)
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{
  "C": {
    "_type": "complex_ndarray",
    "_dtype": "complex128",
    "_value": {
      "imag": [
        [
          1.6800000000000002,
          -0.40999999999999986,
          -1.21,
          0.27999999999999997,
          -0.20999999999999996
        ],
        [
          -1.4900000000000002,
          -1.6000000000000003,
          0.8200000000000001,
          2.1900000000000004,
          1.82
        ],
        [
          1.0599999999999998,
          -1.1199999999999999,
          -1.35,
          -0.6200000000000001,
          0.55
        ]
      ],
      "real": [
        [
          -0.81,
          -0.029999999999999916,
          0.2400000000000001,
          0.7700000000000002,
          -1.1400000000000001
        ],
        [
          -1.0100000000000002,
          0.19000000000000003,
          0.94,
          1.11,
          -0.1899999999999999
        ],
        [
          0.14,
          -0.7999999999999999,
          -0.05999999999999994,
          0.99,
          -0.15999999999999992
        ]
      ]
    }
  }
}
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