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When is a matrix a difference of two idempotents
Linear and Multilinear Algebra, 1990Necessary and sufficient conditions are given for a matrix A to be a sum or a difference of two idempotents. These conditions are expressed in terms of (i) the block structure of A under similarity, as well as (ii) the elementary divisor structure of A.
Robert E. Hartwig, Mohan S. Putcha
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The Symmetrical Idempotent Matrix in Factor Analysis
The Journal of Experimental Education, 1951It is of interest to note the occurrence in facI tor analysis of the symmetrical idempotent ma trix and to examine the role it may play as a mul tiplier of other matrices. For example, Holzin ger and Harman's method of relating two differ ent factorial solutions of the same correlation ma trix1 may be formulated, alternatively, in terms of the ...
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Balanced systems of primitive idempotents in matrix algebras
Sbornik: Mathematics, 2000Let \(A\) be a complex semisimple finite-dimensional associative algebra. The author defines a `balanced \(t\)-system' to be any family \({\mathcal E}=\{e_1,\dots,e_v\}\) of idempotents in \(A\) such that (i) \(e_1+\cdots+e_v\) is a multiple of the identity \(1_A\), and (ii) for any \(s\leq t\), and for any \(s\)-subset \(e_{i_1},\dots,e_{i_s}\) of ...
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Properties of Idempotent Matrix
Econometric Theory, 1997Robert E. Hartwig, Götz Trenkler
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Semicentral idempotents of upper triangular matrix rings
Journal of Algebra and Its ApplicationsIn this paper, we describe the necessary and sufficient conditions for upper triangular [Formula: see text] matrix over a ring to be left (right) semicentral idempotent. Circle compositions of left and right semicentral idempotent matrices ([Formula: see text]) are considered. Many researchers deal with the problems of expressing various matrices as a
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Order Invariability of Idempotent Matrix
Econometric Theory, 1997K. Han, E. Im, M.S. Snow
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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