1. An efficient eigenspace updating scheme for high-dimensional systemsSimon Gangl, Domen Mongus, Borut Žalik, 2014, izvirni znanstveni članek Opis: Systems based on principal component analysis have developed from exploratory data analysis in the past to current data processing applications which encode and decode vectors of data using a changing projection space (eigenspace). Linear systems, which need to be solved to obtain a constantly updated eigenspace, have increased significantly in their dimensions during this evolution. The basic scheme used for updating the eigenspace, however, has remained basically the same: (re)computing the eigenspace whenever the error exceeds a predefined threshold. In this paper we propose a computationally efficient eigenspace updating scheme, which specifically supports high-dimensional systems from any domain. The key principle is a prior selection of the vectors used to update the eigenspace in combination with an optimized eigenspace computation. The presented theoretical analysis proves the superior reconstruction capability of the introduced scheme, and further provides an estimate of the achievable compression ratios. Ključne besede: eigenspace, projection space, data compression, principal component analysis Objavljeno v DKUM: 10.07.2015; Ogledov: 1492; Prenosov: 92
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2. On some equations in prime ringsMaja Fošner, Joso Vukman, 2007, izvirni znanstveni članek Opis: The main purpose of this paper is to prove the following result. Let ▫$R$▫ be a prime ring of characteristic different from two and let ▫$T : R to R$▫ be an additive mapping satisfying the relation ▫$T(x^3) = T(x)x^{2} - xT(x)x + x^{2} T(x)$▫ for all ▫$x in R$▫. In this case ▫$T$▫ is of the form ▫$4T(x) = qx + xq$▫, where ▫$q$▫ is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections. Ključne besede: matematika, algebra, prakolobar, polprakolobar, funkcijska identiteta, odvajanje, jordansko odvajanje, involucija, bicirkularni projektor, mathematics, algebra, prime ring, semiprime ring, functional identity, derivation, Jordan derivation, involution, bicircular projection Objavljeno v DKUM: 10.07.2015; Ogledov: 1398; Prenosov: 85
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3. Some functional equations on standard operator algebrasAjda Fošner, Joso Vukman, 2008, izvirni znanstveni članek Opis: Naj bo ▫$H$▫ kompleksni Hilbertov prostor, ▫$mathcal{B}(H)$▫ algebra vseh omejenih linearnih operatorjev na ▫$H$▫ ter ▫$mathcal{A}(H)$▫ standardna operatorska algebra, zaprta za adjungiranje. Če je ▫$T: mathcal{A}(H) to mathcal{B}(H)$▫ linearna preslikava, ki zadošča identiteti ▫$T(AA^ast A) = T(A)A^ast A - AT(A^ast)A + AA^ast T(A)$▫ za vsak ▫$A$▫ iz ▫$mathcal{A}(H)$▫, potem je ▫$T(A) = AB + BA$▫ za vsak ▫$A$▫ iz A(H), kjer je ▫$B$▫ operator iz ▫$mathcal{B}(H)$▫. Ključne besede: matematika, algebra, kolobar, prakolobar, polprakolobar, Banachov prostor, Hilbertov prostor, standardna operatorska algebra, odvajanje, jordansko odvajanje, bicirkularni projektor, mathematics, algebra, ring, ▫$^ast$▫-ring, prime ring, semiprime ring, Banach space, Hilbert space, standard operator algebra, derivation, Jordan derivation, bicircular projection Objavljeno v DKUM: 10.07.2015; Ogledov: 1406; Prenosov: 100
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4. G-invariant norms and bicircular projectionsMaja Fošner, Dijana Ilišević, Chi-Kwong Li, 2007, izvirni znanstveni članek Opis: It is shown that for many finite dimensional normed vector spaces ▫$V$▫ over ▫$Cc$▫, a linear projection ▫$P: V to V$▫ will have nice structure if ▫$P + lambda (I-P)$▫ is an isometry for some complex unit not equal to one. From these results, one can readily determine the structure of bicircular projections, i.e., those linear projections ▫$P$▫ such that ▫$P + mu (I - P)$▫ is an isometry for every complex unit ▫$mu$▫. The key ingredient in the proofs is the knowledge of the isometry group of the given norm. The proof techniques also apply to real vector spaces. In such cases, characterizations are given to linear projections ▫$P$▫ such that ▫$P - (I - P) = 2P - I$▫ is an isometry. Ključne besede: bicircular projection, symmetric norms, unitarily invariant norms, unitary congruence invariant norms, unitary similarity invariant norms Objavljeno v DKUM: 10.07.2015; Ogledov: 1157; Prenosov: 104
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5. On some functional equations in ringsMaja Fošner, Joso Vukman, 2011, izvirni znanstveni članek Opis: In this article we prove the following result. Let ▫$n ge 1$▫ be some fixed integer, and let ▫$R$▫ be a prime ring with ▫$2n le char(R) ne 2$▫. Suppose there exists an additive mapping ▫$T: R to R$▫ satisfying the relation ▫$T(x^{2n+1}) = sum_{i=1}^{2n+1}(-1)^{i+1} x^{i-1} T(x)x^{2n+1-i}$▫ for all ▫$x in R$▫. In this case, ▫$T$▫ is of the form ▫$4T(x) = qx + xq$▫ for all ▫$x in R$▫, where ▫$q$▫ is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections. Ključne besede: bicircular projection, derivation, functional identity, Jordan tripple derivation, prime ring, ring with involution, semiprime ring Objavljeno v DKUM: 07.06.2012; Ogledov: 1366; Prenosov: 99
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