# ApCoCoA-1:Num.SimDiag

## Num.SimDiag

Computes an approximate diagonalization of a set of matrices.

### Syntax

```Num.SimDiag(A:LIST, MaxIt:INT):[B:MAT, C:MAT]
```

### Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

This function returns a list of two matrices, containing the approximate (almost) eigenvectors of the matrices in A and its inverse.

• @param A A list of quadratic matrices with rational entries.

• @param MaxIt The maximum number of iterations.

• @return The output is a list of two matrices [B:MAT, C:MAT]. The first matrix B contains the real almost eigenvectors of the matrices in A. The matrix C is the inverse of B.

#### Example

```M1 := Mat([[0, 0, -0.079, -0.018],[0, 0,  0.032, -0.012], [1, 0,  1.056, -0.012],[0, 1, -0.060,  1.025]]);
M2 := Mat([[0, -0.063, 0, -0.018],[1,  1.026, 0, -0.012], [0, 0, 0, -0.012], [0, 0, 1, 1.025]]);
M1 := Transposed(M1);
M2 := Transposed(M2);
Result := Num.SimDiag([M1,M2],10);

Dec(Result[2]*M1*Result[1],3);
Dec(Result[2]*M2*Result[1],3);

Mat([
["0.062", "0.016", "0.000", "0.006"],
["0.021", "0.030", "-0.002", "-0.000"],
["0.000", "0.005", "1.006", "-0.035"],
["-0.000", "-0.000", "-0.031", "0.982"]
])
-------------------------------
Mat([
["0.048", "0.000", "0.030", "-0.005"],
["0.000", "0.991", "-0.002", "-0.021"],
["0.020", "0.005", "0.029", "-0.000"],
["0.000", "-0.030", "-0.000", "0.982"]
])
-----------------------------
```