Matrix eigenvalue online calculation tool

Error code = -1: indicates normal completion. If more than 30 iterations are needed, the eigenvalues need to be determined.

Error code > 0 If more than 30 iterations require a defined feature value, the subroutine ends. The error code gives an index of the characteristic value of the failure.

Eigenvalue λ error code + 1 , λ error code + 2 , . . . λ N should be correct, but no eigenvector calculation.

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Eigenvalue and feature vector calculator

λ is the eigenvalue (scalar) of the matrix [A], if there is a non-zero vector (V), so that the following relationship is satisfied:

[A](v) = λ (v)

Each vector (V) satisfies this equation and is called [A] eigenvector λ belonging to the eigenvalue

as an example, in the case of a 3×3 matrix and a 3-item column vector,	and each feature vector is takenv1, v2, v3form of
a11 a12 a13 (A) = a21 a22 a23 　 　 a31 a32 a33	V1 (V) = V2 　 　 V3

How to use this utility?

The first item in (i) is the system, N remember that N should be no more than 12.

(ii) The next N×N item should be a coefficient of a matrix.

The coefficients should be entered in the following order:

a11, a12, a13, . . .

a21, a22, a23, . . .

etc.

Do not enter commas, periods, letters, parentheses, etc.

For example, suppose we want to calculate the eigenvalues and eigenvectors of a 3 × 3 matrix. The data should be entered into the box format as follows:

3
1	2	3
2	-1	1
3	4	-1

Once all the data has been entered, click on the Solve button and the feature vector associated with the feature value and feature [A] will be calculated. Note that a value is assumed to be a real number, but the solution can be complicated. In other words, this calculator can have a imaginary part (the indicated "i") solution, but it assumes that the input is a real number (it cannot accept complex inputs).

important! How to use this output.

If the i-th eigenvalue is a real number, the corresponding eigenvector contained in the i-th column of the vector matrix. .

If the i-th eigenvalue has a complex positive imaginary part, the columns i and (i +1) contain the real and imaginary parts of the corresponding feature vector. The conjugate of this vector is the conjugate eigenvalue of the eigenvector.

Please pay attention to the error code. If it is not equal to -1, some eigenvalues and eigenvector calculations are meaningless.

 

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