# Linear Algebra and its Applications

Linear Algebra and Its Applications > 1995 > 214 > 215-224

^{n}→ K

^{n}defined on the family K

^{n}of all compact, convex, and nonempty sets in R

^{n}is said to be a face mapping if it is additive, and if for every A, S(A) is its face. It is known that if S assumes as its values only 0-dimensional faces, then there exists a lexicographical order on R

^{n}such that for every A, a unique member of S(A) is the greatest...

Linear Algebra and Its Applications > 1995 > 214 > 133-143

Linear Algebra and Its Applications > 1995 > 214 > 193-213

Linear Algebra and Its Applications > 1995 > 214 > 145-185

_{q}-elementary factors play a key role in the context of the matricial version of the classical Caratheodory interpolation problem. Extending work of I. V. Kovalishina, we derive various one-to-one correspondences between Potapov-normalized full-rank J

_{q}-elementary factors and finite nondegenerate q q Caratheodory sequences.

Linear Algebra and Its Applications > 1995 > 214 > 1-10

^{-}

^{1}, where S is quasistochastic. We obtain a necessary and sufficient condition for a given complex matrix A to be stochastically similar to a matrix with any diagonal elements the sum of which equals trace A. Then an inverse elementary divisor result for quasistochastic...

Linear Algebra and Its Applications > 1995 > 214 > 271-275

Linear Algebra and Its Applications > 1995 > 214 > 247-270

_{i}): a

_{i}x

_{i}0 (mod d)} where thea

_{i}'s and d are integers and 0 ≤ a

_{i}< d. Let L,L

_{1}, L

_{2}(B) be lattices over...

Linear Algebra and Its Applications > 1995 > 214 > 17-42

_{k}

_{→}

_{∞}k( )

^{1}

^{k}, where

_{k}( ) = sup{ρ(A

_{1}A

_{2}A

_{k}): each A

_{i}}. Thejoint spectral radius ( ) is circ;( ) = lim sup

_{k}

_{→}

_{∞}circ;

_{k}( )

^{1}

^{k}, where circ;( ) = sup{ A

_{1}A

_{k}: eachA

_{i}...

Linear Algebra and Its Applications > 1995 > 214 > 225-246

Linear Algebra and Its Applications > 1995 > 214 > 119-131

Linear Algebra and Its Applications > 1995 > 214 > 11-16

_{A}(M), where M is a finitely generated, faithful, indecomposable A-module. Guralnick asked whether B must equal A if B is an intermediate algebra of A, i.e., if the A- and B-submodules of M are the same. We give a class of examples where this is not the case.

Linear Algebra and Its Applications > 1995 > 214 > 93-101

Linear Algebra and Its Applications > 1995 > 214 > 43-92

^{-}

^{1}= C andYBX

^{-}

^{1}= D. Contragredient equivalence is a common generalization of four basic equivalence relations: similarity, consimilarity, complex orthogonal...

Linear Algebra and Its Applications > 1995 > 214 > 187-192

Linear Algebra and Its Applications > 1995 > 214 > 103-118

_{1}S

_{2}and covariance A Σ, an explicit formula for the best quadratic unbiased estimator, (Y), of Σ is obtained, where S

_{i}= {Z

_{i}b

_{i}: R

_{i}b

_{i}=M

_{i}u

_{i}for some u

_{i}} and S

_{1}S

_{2}is the linear span of the set of all xy with...

Linear Algebra and Its Applications > 1995 > 215 > 183-223

Linear Algebra and Its Applications > 1995 > 215 > 21-62

Linear Algebra and Its Applications > 1995 > 215 > 135-159

Linear Algebra and Its Applications > 1995 > 215 > 1-19

_{A}(X) = A - X

^{2}on varieties of fixed rank symmetric, skew-symmetric, and rectangular matrices X are determined. Our results extend earlier ones of Eckart...