A new rank formula for idempotent matrices with applications
نویسندگان
چکیده
A complex square matrix A is said to be idempotent, or a projector, whenever A2 = A; when A is idempotent, and Hermitian (or real symmetric), it is often called an orthogonal projector, otherwise an oblique projector. Projectors are closely linked to generalized inverses of matrices. For example, for a given matrix A the product PA = AA + is well known as the orthogonal projector on the range (column space) of A, where A+ is the Moore-Penrose inverse of A; which is the unique solution of the following four Penrose equations
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