What is idempotent matrix?

An idempotent matrix is a square matrix that, when multiplied by itself, results in the same matrix. In other words, for an idempotent matrix A, the product A*A = A.

Idempotent matrices have several important properties, including:

1. They are symmetric.
2. They have eigenvalues of 0 or 1.
3. They are diagonalizable.
4. They can be used to project vectors onto a subspace.

In practical applications, idempotent matrices are often used in statistics, particularly in the field of multivariate analysis, to represent projection and regression matrices. They are also used in signal processing and control theory.