Linear transformations that preserve a similarity class of matrices

1982 ◽  
Vol 11 (1) ◽  
pp. 19-22 ◽  
Author(s):  
William Watkins
Keyword(s):  
Linear Transformations ◽  
Similarity Class ◽  
Class Of Matrices

scholarly journals Linear transformations of sequences

1936 ◽  
Vol 235 (755) ◽  
pp. 367-414 ◽  
Keyword(s):  
Complex Numbers ◽  
Infinite Matrix ◽  
Linear Transformations ◽  
Limit Points ◽  
Class Of Matrices ◽  
Positive Integers ◽  
The Relationship

Given a sequence j tf8, • • ••• of complex numbers, we denote by § («„) the set of all limit points of the sequence, i.e., the set of all such that lim = l p —>■ oo for some increasing sequence of positive integers If is an infinite matrix, with complex elements, and xx a sequence of complex numbers, then, formally at any rate, we can define another sequence jyK by oo y k ^ A = 1 The object of this paper is to investigate relations between $ (*A) and $ (jvK). In particular we shall be concerned with the following question. Given a class $ of matrices and a set 9ft of complex numbers, what sets £) (jv*) can be generated by sequences (#A) with *x<2ft, M < ® ? t This is a geometrical question concerning the structure of sets of points in the plane. It is therefore natural to suppose that oo lim S aKk = 1 K ► 0 0 A = 1 for every matrix of $ ; for this means only that the relationship between (*A) and $ ( y K) is unchanged by a change of origin

Nonuniform Spatial Deformation of Light Fields by Locally Linear Transformations

2017 ◽  
Vol 36 (4) ◽  
pp. 1
Author(s):  
Clemens Birklbauer ◽  
David C. Schedl ◽  
Oliver Bimber
Keyword(s):  
Light Fields ◽  
Linear Transformations ◽  
Spatial Deformation ◽  
Locally Linear

scholarly journals Interconversion of Plasma Free Thyroxine Values from Assay Platforms with Different Reference Intervals Using Linear Transformation Methods

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 45
Author(s):  
Fanwen Meng ◽  
Jacqueline Jonklaas ◽  
Melvin Khee-Shing Leow
Keyword(s):  
Linear Transformation ◽  
Piecewise Linear ◽  
Equilibrium Dialysis ◽  
Accurate Method ◽  
Reference Intervals ◽  
Thyroid Stimulating Hormone ◽  
Free Thyroxine ◽  
Thyroid Function Tests ◽  
Linear Transformations ◽  
Transformation Methods

Clinicians often encounter thyroid function tests (TFT) comprising serum/plasma free thyroxine (FT4) and thyroid stimulating hormone (TSH) measured using different assay platforms during the course of follow-up evaluations which complicates reliable comparison and interpretation of TFT changes. Although interconversion between concentration units is straightforward, the validity of interconversion of FT4/TSH values from one assay platform to another with different reference intervals remains questionable. This study aims to establish an accurate and reliable methodology of interconverting FT4 by any laboratory to an equivalent FT4 value scaled to a reference range of interest via linear transformation methods. As a proof-of-concept, FT4 was simultaneously assayed by direct analog immunoassay, tandem mass spectrometry and equilibrium dialysis. Both linear and piecewise linear transformations proved relatively accurate for FT4 inter-scale conversion. Linear transformation performs better when FT4 are converted from a more accurate to a less accurate assay platform. The converse is true, whereby piecewise linear transformation is superior to linear transformation when converting values from a less accurate method to a more robust assay platform. Such transformations can potentially apply to other biochemical analytes scale conversions, including TSH. This aids interpretation of TFT trends while monitoring the treatment of patients with thyroid disorders.

scholarly journals Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

2021 ◽  
Vol 2 (5) ◽  
Author(s):  
Soroosh Tayebi Arasteh ◽  
Adam Kalisz
Keyword(s):  
Computer Graphics ◽  
Geometric Design ◽  
The Other ◽  
Control Points ◽  
Complex Surfaces ◽  
Linear Transformations ◽  
Computer Aided Geometric Design ◽  
Cubic Curves ◽  
Original Curve ◽  
Computer Aided

AbstractSplines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

Linear transformations extract parameters of ionic currents and action potential features from pseudo-ECG in cardiomyocyte models

2020 ◽  
Author(s):  
Salim Baigildin ◽  
Konstantin Ushenin ◽  
Aigul Fabarisova ◽  
Marat Bogdanov ◽  
Olga Solovyeva
Keyword(s):  
Action Potential ◽  
Ionic Currents ◽  
Linear Transformations

M-matrix and inverse M-matrix extensions

2020 ◽  
Vol 8 (1) ◽  
pp. 186-203
Author(s):  
J.J. McDonald ◽  
R. Nandi ◽  
K.C. Sivakumar ◽  
P. Sushmitha ◽  
M.J. Tsatsomeros ◽  
...  
Keyword(s):  
Classical Theory ◽  
Class Of Matrices ◽  
New Perspective

AbstractA class of matrices that simultaneously generalizes the M-matrices and the inverse M-matrices is brought forward and its properties are reviewed. It is interesting to see how this class bridges the properties of the matrices it generalizes and provides a new perspective on their classical theory.

scholarly journals Computing the Exact Number of Similarity Classes in the Longest Edge Bisection of Tetrahedra

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1447
Author(s):  
Jose P. Suárez ◽  
Agustín Trujillo ◽  
Tania Moreno
Keyword(s):  
Data Structure ◽  
Stability Condition ◽  
Open Problem ◽  
Integer Arithmetic ◽  
Exact Number ◽  
Similarity Class ◽  
The Stability ◽  
High Level ◽  
The Cost

Showing whether the longest-edge (LE) bisection of tetrahedra meshes degenerates the stability condition or not is still an open problem. Some reasons, in part, are due to the cost for achieving the computation of similarity classes of millions of tetrahedra. We prove the existence of tetrahedra where the LE bisection introduces, at most, 37 similarity classes. This family of new tetrahedra was roughly pointed out by Adler in 1983. However, as far as we know, there has been no evidence confirming its existence. We also introduce a new data structure and algorithm for computing the number of similarity tetrahedral classes based on integer arithmetic, storing only the square of edges. The algorithm lets us perform compact and efficient high-level similarity class computations with a cost that is only dependent on the number of similarity classes.

Sign in / Sign up

Export Citation Format

Share Document