The determinant of a matrix is a function whose input is a matrix, and whose output is a scalar quantity. This quantity is called the determinant, and it is used for determining many things about a matrix, including its eigenvalues, eigenvectors, and characteristic polynomial....
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....
No, not every matrix has an inverse. A matrix must be square (i.e. have the same number of rows and columns) and have a non-zero determinant in order to have an inverse. If the determinant is zero, the matrix is said to be singular and cannot be inverted. ...
V.N. KublanovskayaElsevier B.V.USSR Computational Mathematics and Mathematical PhysicsV. N. Kublanovskaya, “Newton’s method for finding eigenvalues and eigenvectors of a matrix,” Zh. Vychisl. Mat. Mat. Fiz , 12 , No. 6, 1371–1380 (1966)....