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FROBENIUS FULL MATRIX ALGEBRAS AND GORENSTEIN TILED ORDERS
"... Let D be a discrete valuation ring with a unique maximal ideal piD, and let Λ be a Dorder. It is standard to reduce homological properties of Λ to those of the factor algebras Λ/piΛ and such factor algebras are deserving of further study. (See [2].) Let n be an integer with n ≥ 2. In [1], we introd ..."
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introduced an n × n Afull matrix algebra over a field K, whose multiplication is determined by a structure system A, that is, an ntuple of n × n matrices with certain properties. Afull matrix algebras are associative, basic, connected Kalgebras. A prototype of Afull matrix algebras is the class
Shape and motion from image streams under orthography: a factorization method
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1992
"... Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an illconditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orth ..."
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Cited by 1094 (38 self)
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uses the singularvalue decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a
A CALIBRATION ROUTINE FOR FULL MATRIX CAPTURE (FMC)
"... When phased array probes are used for ultrasonic inspection it is necessary to ensure that consistent performance is achieved. If Full Matrix Capture (FMC) is used to record inspection data the most appropriate way of doing this is to assess transducer performance on an element by element basis rath ..."
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When phased array probes are used for ultrasonic inspection it is necessary to ensure that consistent performance is achieved. If Full Matrix Capture (FMC) is used to record inspection data the most appropriate way of doing this is to assess transducer performance on an element by element basis
Unitary Orbits in a Full Matrix Algebra
, 2008
"... The Hilbert manifold Σ consisting of positive invertible (unitized) HilbertSchmidt operators has a rich structure and geometry. The geometry of unitary orbits Ω⊂Σis studied from the topological and metric viewpoints: we seek for conditions that ensure the existence of a smooth local structure for t ..."
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Cited by 3 (2 self)
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The Hilbert manifold Σ consisting of positive invertible (unitized) HilbertSchmidt operators has a rich structure and geometry. The geometry of unitary orbits Ω⊂Σis studied from the topological and metric viewpoints: we seek for conditions that ensure the existence of a smooth local structure for the set Ω, and we study the convexity of this set for the geodesic structures that arise when we give Σ two Riemannian metrics.
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 427 (36 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity
ZnGRADED POLYNOMIAL IDENTITIES OF THE FULL MATRIX ALGEBRA OF ORDER n
, 1999
"... The algebra Mn(F)ofalln×nmatrices over a field F has a natural Zngrading Mn(F) = ∑ ⊕ (α) M α∈Zn n. In this paper graded identities of the Zngraded algebra Mn(F) over a field of characteristic zero are studied. It is shown that all the Zngraded polynomial identities of Mn(F) follow from the fol ..."
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The algebra Mn(F)ofalln×nmatrices over a field F has a natural Zngrading Mn(F) = ∑ ⊕ (α) M α∈Zn n. In this paper graded identities of the Zngraded algebra Mn(F) over a field of characteristic zero are studied. It is shown that all the Zngraded polynomial identities of Mn(F) follow from the following: x1x2 − x2x1 =0, α(x1)=α(x2)=0; x1xx2 − x2xx1 =0, α(x1)=α(x2)=−α(x).
The structure of derivations from a full matrix algebra into its dual
 Iranian J. Sci. Tec, Trans. A
"... Abstract – Let A be a unital algebra over a field of characteristic zero. We show that every derivation from ()nM A into its dual ()nM A ∗ is the sum of an inner derivation and a derivation induced by a derivation from A into A ∗. ..."
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Abstract – Let A be a unital algebra over a field of characteristic zero. We show that every derivation from ()nM A into its dual ()nM A ∗ is the sum of an inner derivation and a derivation induced by a derivation from A into A ∗.
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