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Review of Matrix Algebra
Review of Matrix Algebra

... diagonal (diagonal running from upper left to lower right) if aij  a ji . For example, for a (3x3), we ...
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Concentration of Measure for Block Diagonal Matrices October 2010

... of Q in the measurement space RM . This enables the efficient solution of problems such as finding the nearest neighbor to a point x in a database Q by permitting these problems to be solved in the low-dimensional observation space. The same concentration result has also been used to prove that cert ...
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Just the Factors, Ma`am HAROLD B. REITER http://www.math.uncc

... 3. The geometry of DN . To investigate the geometry of DN , we first explore the relation ‘divides’. Recall that a|b means that a and b are positive integers for which b/a is an integer. The relation ‘|’ has several important properties, three of which are crucial to our discussion. 1. Reflexive. Fo ...
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Chapter 15. The Kernel of a Three-by

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Representations of a finite group in positive characteristic

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MATH 108A HW 6 SOLUTIONS Problem 1. [§3.15] Solution. `⇒` Let

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... 1.5. Characteristic vectors. Now return to the general problem. Values of λ which solve the determinantal equation are called the characteristic roots or eigenvalues of the matrix A. Once λ is known, we may be interested in vectors x which satisfy the characteristic equation. In examining the genera ...
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Real-Time Endmember Extraction on Multicore Processors

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Lecture notes Math 4377/6308 – Advanced Linear Algebra I

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NTH ROOTS OF MATRICES - University of Central Missouri

Section 1: Fields Let us begin with the definition of a field. A field F is
Section 1: Fields Let us begin with the definition of a field. A field F is

< 1 ... 17 18 19 20 21 22 23 24 25 ... 100 >

Perron–Frobenius theorem

In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector can be chosen to have strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory (ergodicity of Markov chains); to the theory of dynamical systems (subshifts of finite type); to economics (Okishio's theorem, Leontief's input-output model); to demography (Leslie population age distribution model), to Internet search engines and even ranking of football teams.
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