Dilations of line in itself as the automorphism of the skew-field constructed over in the same line in Desargues affine plane

2019 ◽  
Vol 13 (5) ◽  
pp. 231-237 ◽  
Author(s):  
Orgest Zaka
Keyword(s):  
Affine Plane ◽  
Skew Field

scholarly journals A necessary and sufficient condition for simultaneous diagonalization of two hermitian matrices and its application

1970 ◽  
Vol 11 (1) ◽  
pp. 81-83 ◽  
Author(s):  
Yik-Hoi Au-Yeung
Keyword(s):  
Complex Numbers ◽  
Single Element ◽  
Singular Matrix ◽  
Necessary And Sufficient Condition ◽  
Simultaneous Diagonalization ◽  
Hermitian Matrices ◽  
Skew Field ◽  
Conjugate Transpose ◽  
Necessary And Sufficient ◽  
Real Quaternions

We denote by F the field R of real numbers, the field C of complex numbers, or the skew field H of real quaternions, and by Fn an n dimensional left vector space over F. If A is a matrix with elements in F, we denote by A* its conjugate transpose. In all three cases of F, an n × n matrix A is said to be hermitian if A = A*, and we say that two n × n hermitian matrices A and B with elements in F can be diagonalized simultaneously if there exists a non singular matrix U with elements in F such that UAU* and UBU* are diagonal matrices. We shall regard a vector u ∈ Fn as a l × n matrix and identify a 1 × 1 matrix with its single element, and we shall denote by diag {A1, …, Am} a diagonal block matrix with the square matrices A1, …, Am lying on its diagonal.

On a conjecture of Hughes

1967 ◽  
Vol 63 (3) ◽  
pp. 647-652 ◽  
Author(s):  
Judita Cofman
Keyword(s):  
Projective Plane ◽  
Permutation Group ◽  
Translation Plane ◽  
Collineation Group ◽  
Affine Plane ◽  
Finite Projective Plane ◽  
Transitive Permutation Group ◽  
Condition C

D. R. Hughes stated the following conjecture: If π is a finite projective plane satisfying the condition: (C)π contains a collineation group δ inducing a doubly transitive permutation group δ* on the points of a line g, fixed under δ, then the corresponding affine plane πg is a translation plane.

Bayesian Nash Equilibrium in Electricity Spot Markets: An Affine-Plane Approximation Approach

2021 ◽  
pp. 1-1
Author(s):  
Pranjal Pragya Verma ◽  
Mohammad Hesamzadeh ◽  
Ross Baldick ◽  
Darryl Biggar ◽  
K. Shanti Swarup ◽  
...  
Keyword(s):  
Nash Equilibrium ◽  
Affine Plane ◽  
Spot Markets ◽  
Approximation Approach ◽  
Bayesian Nash Equilibrium ◽  
Electricity Spot Markets

An example of a skew field without a trace

1989 ◽  
Vol 17 (9) ◽  
pp. 2303-2307 ◽  
Author(s):  
L. Makar-Limanov
Keyword(s):  
Skew Field

scholarly journals HIGHER PRODUCT PYTHAGORAS NUMBERS OF SKEW FIELDS

2010 ◽  
Vol 03 (01) ◽  
pp. 193-207
Author(s):  
Dejan Velušček
Keyword(s):  
Laurent Series ◽  
Skew Field ◽  
Skew Fields ◽  
Pythagoras Number

We introduce the n–th product Pythagoras number p n(D), the skew field analogue of the n–th Pythagoras number of a field. For a valued skew field (D, v) where v has the property of preserving sums of permuted products of n–th powers when passing to the residue skew field k v and where Newton's lemma holds for polynomials of the form Xn - a, a ∈ 1 + I v , p n(D) is bounded above by either p n( k v ) or p n( k v ) + 1. Spherical completeness of a valued skew field (D, v) implies that the Newton's lemma holds for Xn - a, a ∈ 1 + I v but the lemma does not hold for arbitrary polynomials. Using the above results we deduce that p n (D((G))) = p n(D) for skew fields of generalized Laurent series.

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