Vector Spaces of Magic Squares

1980 ◽  
Vol 53 (2) ◽  
pp. 108 ◽  
Author(s):  
James E. Ward
Keyword(s):  
Vector Spaces ◽  
Magic Squares

scholarly journals Vector Spaces of New Special Magic Squares: Reflective Magic Squares, Corner Magic Squares, and Skew-Regular Magic Squares

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Thitarie Rungratgasame ◽  
Pattharapham Amornpornthum ◽  
Phuwanat Boonmee ◽  
Busrun Cheko ◽  
Nattaphon Fuangfung
Keyword(s):  
Linear Algebra ◽  
Standard Addition ◽  
Scalar Multiplication ◽  
Vector Spaces ◽  
Magic Squares ◽  
Magic Square ◽  
Definition Of

The definition of a regular magic square motivates us to introduce the new special magic squares, which are reflective magic squares, corner magic squares, and skew-regular magic squares. Combining the concepts of magic squares and linear algebra, we consider a magic square as a matrix and find the dimensions of the vector spaces of these magic squares under the standard addition and scalar multiplication of matrices by using the rank-nullity theorem.

From Magic Squares To Vector Spaces

1982 ◽  
Vol 75 (1) ◽  
pp. 76-77
Author(s):  
Martin P. Cohen ◽  
John Bernard
Keyword(s):  
Vector Spaces ◽  
Magic Squares

Those number squares offer an opportunity to study structure.

Vector Spaces of Magic Squares

1980 ◽  
Vol 53 (2) ◽  
pp. 108-111 ◽  
Author(s):  
James E. Ward
Keyword(s):  
Vector Spaces ◽  
Magic Squares

scholarly journals Quadrados mágicos: um passeio pela História e pela Álgebra Linear

2018 ◽  
Vol 40 ◽  
pp. 54
Author(s):  
Marcelo Ferreira de Melo ◽  
José Samuel Machado
Keyword(s):  
Higher Education ◽  
High School ◽  
Linear Systems ◽  
Vector Spaces ◽  
Magic Squares ◽  
Historical Aspects

The objective of this work is to study the magic squares, to address historical aspects related to their emergence and their use by artists throughout the centuries, as well as to analyze the magic squares in the resolution of linear systems and in the language of the vector spaces of matrices. As a result, one can obtain another motivation for the study of matrices and linear systems, both in High School and Higher Education.

Model Based Defect Detection in Multi-Dimensional Vector Spaces

2011 ◽  
Vol 131 (9) ◽  
pp. 1633-1641
Author(s):  
Toshifumi Honda ◽  
Kenji Obara ◽  
Minoru Harada ◽  
Hajime Igarashi
Keyword(s):  
Defect Detection ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Model Based

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

Stable and Supported Semantics in Continuous Vector Spaces

2020 ◽  
Author(s):  
Yaniv Aspis ◽  
Krysia Broda ◽  
Alessandra Russo ◽  
Jorge Lobo
Keyword(s):  
Logic Program ◽  
Matrix Multiplication ◽  
Vector Spaces ◽  
Continuous Space ◽  
Continuous Vector ◽  
Novel Approach ◽  
Gradient Based ◽  
Normal Logic ◽  
Parameter Values ◽  
Normal Logic Program

We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.

Sign in / Sign up

Export Citation Format

Share Document