Change the matrix from p to diagonal matrix to find p: after getting the eigenvalue, substitute it into the characteristic equation to find the basic solution system, get the eigenvector, and then get the orthogonal matrix p through Schmidt orthogonalization.

P is a matrix formed by orthogonalization and unitization of the characteristic vector of A, which is exactly the same as the solution of P in the similar diagonalization of A. Because A is a real symmetric matrix, there must be an orthogonal matrix P (the inverse of P is the transposition of P) to change A into a diagonal matrix. Under the condition that A can be diagonalized, P is a matrix in which the eigenvectors of A are arranged in the order of eigenvalues.

matrix

It is a common tool in applied mathematics disciplines such as advanced algebra and statistical analysis. In physics, matrices have applications in circuit science, mechanics, optics and quantum physics. In computer science, three-dimensional animation also needs matrix. Matrix operation is an important problem in the field of numerical analysis. Decomposition of a matrix into a combination of simple matrices can simplify the operation of the matrix in theory and practical application.