Extending Hierarchical Probing for Computing the Trace of Matrix Inverses

2020 ◽  
Vol 42 (3) ◽  
pp. A1459-A1485
Author(s):  
Jesse Laeuchli ◽  
Andreas Stathopoulos
Keyword(s):  
Trace Of Matrix

On the Trace of Matrix Products

1959 ◽  
Vol 20 (3-6) ◽  
pp. 171-174 ◽  
Author(s):  
Leon Mirsky
Keyword(s):  
Matrix Products ◽  
Trace Of Matrix

Inequalities for the trace of matrix product

1994 ◽  
Vol 39 (12) ◽  
pp. 2489-2490 ◽  
Author(s):  
Yuguang Fang ◽  
K.A. Loparo ◽  
Xiangbo Feng
Keyword(s):  
Matrix Product ◽  
Trace Of Matrix

An inequality for the trace of matrix products

1974 ◽  
Vol 6 (2) ◽  
pp. 225-235 ◽  
Author(s):  
H.W Capel ◽  
P.A.J Tindemans
Keyword(s):  
Matrix Products ◽  
Trace Of Matrix

VON WILLEBRAND FACTOR RELEASED FROM WEIBEL-PALADE BODIES BINDS MORE AVIDLY TO EXTRACELLULAR MATRIX THAN THAT SECRETED CONSTITUTIVELY

1987 ◽  
Author(s):  
L A Sporn ◽  
V J Marder ◽  
D D Wagner
Keyword(s):  
Extracellular Matrix ◽  
Endothelial Cells ◽  
Von Willebrand Factor ◽  
Starting Material ◽  
Human Foreskin Fibroblasts ◽  
Vitro Model ◽  
Trace Of Matrix ◽  
Von Willebrand ◽  
Willebrand Factor

Large multimers of von Willebrand factor (vWf) are released from the Weibel-Palade bodies (WPB) of cultured endothelial cells following treatment with a secretagogue, whereas predominantly dimeric forms are secreted constitutively. These two pools of vWf were used to compare binding of the various multimeric forms of vWf to the extracellular matrix (ECM), the in vitro model of the basement membrane. The released multimers and an equal number of subunits of constitutively secreted vWf were placed, for 72 hours, on cultures of human foreskin fibroblasts (HFF) grown on glass coverslips, then fixed and stained by fluorescence using anti-vWf antiserum. Constitutively secreted vWf produced only a trace of matrix decoration, whereas the released large multimers bound more extensively. In order to determine if increased binding of released vWf was due to the presence of another component in the releasate, releasate from which vWf was adsorbed was combined with constitutively secreted vWf, and this mixture was overlaid onto HFF. The presence of the adsorbed releasate did not promote binding of constitutively secreted vWf. Therefore, it appears that the enhanced binding observed was due to the large multimeric size of vWf stored in the WPB. To further substantiate this, iodinated plasma vWf which was presumably constitutively secreted from endothelial cells was overlaid on.to HFF for 72 hours, labeled vWf was removed, and cells were washed extensively and lysed. Samples of iodinated plasma vWf (starting material) and cell lysates were e1ectrophoresed, non-reduced on an agarose gel. Densitometric scans of starting material and of bound vWf revealed that the large multimeric forms bound preferentially. It appears that multivalency is likely an important property in vWf interaction with the ECM, just as has been shown for vWf interaction with platelets. The pool of vWf contained within the WPBs, therefore, is not only especially suited for platelet interaction, but also for interaction with the ECM.

An inequality for the trace of matrix product

1992 ◽  
Vol 37 (2) ◽  
pp. 239-240 ◽  
Author(s):  
J.K. Baksalary ◽  
S. Puntanen
Keyword(s):  
Matrix Product ◽  
Trace Of Matrix
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