Displaying similar documents to “Affine invariant contractions of simplices”

Laplace Expansion

Karol Pak, Andrzej Trybulec (2007)

Formalized Mathematics

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In the article the formula for Laplace expansion is proved.

Restricted estimation in unbalanced factorial models: an APL programs package.

José M. Prieto, José M. Caridad (1988)

Qüestiió

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This paper describes a set of programs that provide researchers with restricted effect estimations in unbalanced factorial models when several weighing systems are imposed upon those models. The main program performing such an analysis is known as REUFM, and is written in APL⊗PLUS for IBM/PC microcomputers. An example is given in order to ilustrate the programs.

The theory and applications of complex matrix scalings

Rajesh Pereira, Joanna Boneng (2014)

Special Matrices

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We generalize the theory of positive diagonal scalings of real positive definite matrices to complex diagonal scalings of complex positive definite matrices. A matrix A is a diagonal scaling of a positive definite matrix M if there exists an invertible complex diagonal matrix D such that A = D*MD and where every row and every column of A sums to one. We look at some of the key properties of complex diagonal scalings and we conjecture that every n by n positive definite matrix has at...

Basic Properties of the Rank of Matrices over a Field

Karol Pąk (2007)

Formalized Mathematics

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In this paper I present selected properties of triangular matrices and basic properties of the rank of matrices over a field.I define a submatrix as a matrix formed by selecting certain rows and columns from a bigger matrix. That is in my considerations, as an array, it is cut down to those entries constrained by row and column. Then I introduce the concept of the rank of a m x n matrix A by the condition: A has the rank r if and only if, there is a r x r submatrix of A with a non-zero...