A symmetric real matrix admits only real eigenvalues. We show how one can find these eigenvalues as well as their corresponding eigenvectors without using Mathematica's built-in commands (Eigenvalues and Eigenvectors). This iterative technique is described in great details in the book by Kenneth J....
The rest of this work is organized as follows. In Section2, we provide some basic theory on commuting families and eigenvalue condition numbers. In Section3we present our main algorithm (Algorithm 1) that uses a random linear combination to extract eigenvectors, followed by one- and two-sided...
The above process (2.6) can be easily extended to the oversampled case, in whichL>m+n+1and the matrixCabove is of sizeL\times (m+n+2). In this case the matrix in (2.6) has at least as many rows as columns, and does not necessarily have a null vector. Then the task is to ...
Then instead of SVD you just find the eigenvectors of a 4×4 symmetric matrix, which is about 30% cheaper than SVD of 3×3 matrix. Also you don’t have to worry about handling special cases like reflections as in the SVD method. Check the Horn original paper: http://people.csail.mit...
in finding riccati solution of A*X+A'*X+X*W*X+Q that is X which stabilises A+W*X(real parts of eigen values are 0) This can be possible If...
where “A” represents a diagonal matrix comprising the eigenvalues and “V” is another matrix including the analogous eigenvectors. Subsequently, V can be separated. Hence, it can be practiced in an equation that produces a sort of pseudo spectrum, causing a peak at the arrival angle of the...