(k,l,t)-idempotent Matrix In The Application Of Multivariate Statistical Analysis

(k,l,t)-idempotent matrix is used frequently as a kind of special matrix, no matter in matrix theory or in probability theory. So research on this aspect, already become a hot issue at home and abroad.In the background of the hot study on (k,l,t)-idempotent matrix, apply the (k,l,t)-idempotent matrix’s nature of diagonalization to prove 2-idempotent of (3,1,1)-idempotent matrix and an arbitrary matrix linear combination, according to the retention of (k,l,t)-idempotent matrix. Then present the generalized idempotent of (3,l,1)-idempotent matrix and arbitrary matrix linear combination, obey analogy method, enrich and expand this research. Then further study the application of (k,l,t)-idempotent matrix. By the features of characteristic value of (k,l,t)-idempotent matrix, the nature of χ2 distribution and characteristic function, get an application of theorem of (2,1,1)-idempotent matrix in multivariate statistical analysis. And get the application of theorem of (k,l,t)-idempotent matrix in multivariate statistical analysis, obey analogy method. Open up the new angle on (k,l,t)-idempotent matrix.