Abstract
The Sri Lankan Journal of Applied Statistics(SLJAS) is an open-access, international, double-blind peer-reviewed journal published by the Institute of Applied Statistics, Sri Lanka (IASSL). The main purpose of the journal is to publish the results of original work on applications of Statistics and on theoretical and methodical aspects of Statistics. The journal also welcomes critical reviews including conceptual discussions, opinions and book reviews. Applications of Statistics in the area of Agriculture & Forestry, Medical, Dental and Veterinary Sciences, Natural, Physical Sciences, Social Sciences, Economics and Actuarial Science fall within the scope of the journal. This journal does not charge any fee for article processing and submission.
Highlights
An n×n matrix A is called idempotent if A = A2
We begin with a customary linear model Y = Xβ + ε where Yn×1 is a response vector, Xn×r is a known design matrix of real numbers, βr×1 is an unknown vector of regression parameters, and εn×1 is the error vector with E[ε] = 0 and V[ε] = σ2In×n
We first propose a construction in the light of (2.1) where X is an arbitrary real matrix of rank r
Summary
Tr A2A†A∗ ≥ ρ(A), and the equality holds if and only if A is idempotent These rather well-known results, do not render immediate help in exhibiting concrete but non-trivial idempotent matrices quickly. We provide cute ideas to come up with non-trivial and concrete idempotent matrices quickly and efficiently. The point is that one must exhibit some appropriate projection matrix An×n with a specified rank r(< n), both quickly and explicitly.
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