Convex matrix optimization problems with low-rank solutions play a fundamental role in signal processing, statistics, and related disciplines. These problems are difficult to solve because of the cost of maintaining the matrix decision variable, even though the low-rank solution has few degrees of freedom. This talk presents an algorithm that pr...
Creator:
Tropp, Joel (California Institute of Technology)
Created:
2018-04-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The purpose of this tutorial is to describe the intellectual apparatus that supports some modern techniques in statistics, machine learning, signal processing, and related areas. The main ingredient is the observation that many types of data admit parsimonious representations, i.e., there are far fewer degrees of freedom in the data than the amb...
Creator:
Tropp, Joel (California Institute of Technology)
Created:
2011-09-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We introduce a new methodology for studying the maximum eigenvalue of a sum of independent, symmetric random matrices. This approach results in a complete set of extensions to the classical tail bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Freedman, Hoeffding, and McDiarmid. Results for rectangular random matrices follow...
Creator:
Tropp, Joel (California Institute of Technology)
Created:
2011-09-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities,...
Creator:
Tropp, Joel
Created:
2018-04-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Scale. Marble-topped rectangular wooden box scale with mechanism hidden inside of the box; two circular brass pans are resting on intersecting brass arms in the shape of an X emerge from box, curving upwards to support the pans; wooden box has incised linear decoration, and front of box has small circular window that reveals two arrows which ris...
Creator:
Troemner, Henry, 1809-1873
Contributor:
The Henry Troemner Company (Philadelphia, Pennsylvania)
Created:
1866 - 1900?
Contributed By:
University of Minnesota Libraries, Owen H. Wangensteen Historical Library of Biology and Medicine.
Scale. Scale mechanism is encased in a box made from a wooden frame and beveled glass walls; scale mechanism is an equal arm, Roberval balance made of metal with agate bearings; two round metal pans with rectangular, curved handles are supported by the outer two weighing arms emerging from the box; the center column contains a downward pointing ...
Creator:
Troemner, Henry, 1809-1873
Contributor:
The Henry Troemner Company (Philadelphia, Pennsylvania)
Created:
1913 - 1925?
Contributed By:
University of Minnesota Libraries, Owen H. Wangensteen Historical Library of Biology and Medicine.
Scale. Scale mechanism is encased in a box made from a wooden frame and beveled glass walls; scale mechanism is an equal arm, Roberval balance made of metal with agate bearings; two round metal pans with rectangular, curved handles are supported by the outer two weighing arms emerging from the box; the center column contains a downward pointing ...
Creator:
Troemner, Henry, 1809-1873
Contributor:
The Henry Troemner Company (Philadelphia, Pennsylvania)
Created:
1913 - 1925?
Contributed By:
University of Minnesota Libraries, Owen H. Wangensteen Historical Library of Biology and Medicine.