A matrix is a linear transformation.
Singular value decomposition is a method with obvious physical meaning. It can represent a relatively complex matrix by multiplying several smaller and simpler sub-matrices. These small matrices describe the important characteristics of the matrix. .
The purpose of eigenvalue decomposition and singular value decomposition is to extract the representative and important features of the matrix.
1 Eigenvalue :
If a vector v is an eigenvector of a square matrix A, it must be expressed in the following form:
At this time, λ is called the eigenvalue corresponding to the eigenvector v, and a set of eigenvectors of a matrix is a set of orthogonal vectors. Eigenvalue decomposition is to decompose a matrix into the following form:
Where Q is a matrix composed of the eigenvectors of this matrix A, Σ is a diagonal matrix, and each diagonal element is an eigenvalue.
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