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Call your matrix A, the eigenvalues are defined as the numbers e for which a nonzero vector v exists such that Av = ev. This is equivalent to requiring (A-eI)v=0 to have a non zero solution v, where I is the identity matrix of the same dimensions as A. A matrix A-eI with this property is called singular and has a zero determinant. The determinant of A-eI is a polynomial in e, which has the eigenvalues of A as roots. Often setting this polynomial to zero and solving for e is the easiest way to compute the eigenvalues of A.
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Can a Hermitian Matrix possess Complex Eigenvectors?
Yes. Simple example: a=(1 i) (-i 1) The eigenvalues of the Hermitean matrix a are 0 and 2 and the corresponding eigenvectors are (i -1) and (i 1). A Hermitean matrix always has real eigenvalues, but it can have complex eigenvectors.
A c program to find maximum number in a 3 by 3 matrix?
int matrix[][]; // the matrix to find the max in int max = matrix[0][0]; int r,c; for(r = 0; r < 3; ++r) { for(c = 0; c < 3; ++c) { if(matrix[r][c] > max) { max = matrix[r][c]; } } } // max is now the maximum number in matrix
How do you find a negative matrix in algebra?
For example, if you have [ -4 1 0 3] as your matrix, it would be negative 4. Whatever negative number is in your matrix is your answer.
What are eigenvalues and eigenvectors?
An eigenvector is a vector which, when transformed by a given matrix, is merely multiplied by a scalar constant; its direction isn't changed. An eigenvalue, in this context, is the factor by which the eigenvector is multiplied when transformed.
Do similar matrices have the same eigenvalues?
Yes, similar matrices have the same eigenvalues.
