Matrix zeros of polynomials

2020 ◽  
Vol 104 (559) ◽  
pp. 27-35
Author(s):  
Damjan Kobal
Keyword(s):  
Linear Algebra ◽  
Zeros Of Polynomials ◽  
University Mathematics ◽  
Easy Proof ◽  
New Perspective

The concepts of polynomials and matrices essentially expand and enhance the elementary arithmetic of numbers. Once introduced, polynomials and matrices open up new interesting mathematical challenges which extend to new fields of mathematical explorations within university mathematics. We present an aspect of a rather elementary exploration of polynomials and matrices, which offers a new perspective and an interesting matrix analogue to the concept of a zero of a polynomial. The discussion offers an opportunity for better comprehension of the fundamental concepts of polynomials and matrices. As an application we are led to the meaningful questions of linear algebra and to an easy proof of the otherwise advanced and abstract Cayley-Hamilton theorem.

scholarly journals Study On Ideological And Political Education Of Linear Algebra Course

2021 ◽  
Vol 07 (10) ◽  
Author(s):  
LIU Xian-bei ◽  
Keyword(s):  
Linear Algebra ◽  
Colleges And Universities ◽  
Ideological And Political Education ◽  
Engineering Majors ◽  
New Era ◽  
University Mathematics ◽  
Teaching Concept ◽  
Ideological Education ◽  
Basic Course ◽  
Teaching Ideas

To implement the ideological and political teaching concept of curriculum is a key measure to establish morality and cultivate talents in the new era, and also a basic requirement of colleges and universities' original mission of "educating talents for the Party and the country". University mathematics, as a basic subject universally offered in colleges and universities, has advantages in the course of ideological and political teaching, but also has obvious shortcomings. Linear algebra is a compulsory basic course for science and engineering majors, aiming at cultivating students' logical training and abstract thinking ability. This article mainly to the "Linear Algebra" teaching as an example, the first to study the Linear Algebra course ideological education and the advantages of the ideological education into the difficulty in the course, and put forward the linear algebra course ideological education the implementation of the specific methods: update teaching ideas, strengthen the teacher training, teaching methods and build a rich curriculum ideological system of the implementation of the path.

scholarly journals Changes made to the teaching of linear algebra and calculus courses in the UK in response to the COVID-19 pandemic

2021 ◽  
Author(s):  
Maryam Alarfaj ◽  
Steven O'Hagan ◽  
Chris Sangwin
Keyword(s):  
Linear Algebra ◽  
Video Conferencing ◽  
Delivery Mode ◽  
Discussion Forums ◽  
Teaching Activities ◽  
University Mathematics ◽  
Electronic Submission ◽  
Video Clips ◽  
The Uk ◽  
Digital Delivery

In response to the COVID-19 pandemic, university mathematics departments in the UK adapted their teaching for 2020-21, with some courses being delivered digitally and others through a mixture of on-campus and digital delivery. A survey of linear algebra and calculus lecturers was carried out in the spring of 2021 to investigate what changes were made to courses, as well as lecturers’ perceptions of institutional decision making and support. This survey found that a majority of the 41 participants were satisfied that the choice of delivery mode was correct, although views about the importance of offering on-campus classes were mixed. There was a significant increase in the use of video clips made by the lecturer, video-conferencing software, discussion forums, electronic submission of written work and on-screen marking tools. Most lecturers reported a reduction in the amount of time that students were expected to be taking part in live teaching activities and an increase in the amount of time they were expected to be working on asynchronous activities. While some were keen to return to their previous practice, others were enthusiastic about retaining features introduced in response to the COVID-19 pandemic.

Application of Linear Algebra in Real Life

2014 ◽  
Vol 556-562 ◽  
pp. 3392-3395
Author(s):  
Ji Xia Deng
Keyword(s):  
Linear Algebra ◽  
Matrix Theory ◽  
Real Life ◽  
Dimensional Vector ◽  
Transformation Theory ◽  
Dimensional Vector Space ◽  
University Mathematics ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Basic Course

Linear algebra is an important basic course in university mathematics, finite dimensional vector space and linear transformation theory mainly on matrix theory, and the combination of matrix. Concept in linear algebra is defined directly by the mathematical symbol, rarely by example to import. How to make students master the abstract and difficult course, first of all is to let the students find the course in our daily life, to stimulate interest in learning.

scholarly journals Essential Concepts for the First Year of Study for BSc Mathematics

2018 ◽  
Vol 16 (2) ◽  
pp. 16
Author(s):  
Alexander Capes ◽  
Peter Rowlett
Keyword(s):  
Linear Algebra ◽  
First Year ◽  
Undergraduate Mathematics ◽  
Transition To University ◽  
Degree Programme ◽  
Mathematical Writing ◽  
University Mathematics

To inform discussion about content for the first year of undergraduate mathematics, a study was completed which reviewed: the A-level Mathematics specification; published literature on the transition from A-level to university mathematics; the second and third year curricula of modules at three English universities with different foci. This aimed to investigate what students might reasonably be expected to have covered when they arrive at university, what happens in practice at the transition to university, and the role of the first year as preparation for later study. Content suggestions focus on calculus, linear algebra and analysis as core topics. There is also evidence of the need to focus on students' understanding of where formulae and solutions originated as well as their ability to produce pieces of academic and mathematical writing. Findings also include suggestion that what happens in the first year, while similar between institutions, does depend on the overall focus of the degree programme.

SREM observation of the interaction between the in-situ deposited Pd small particles and MgO cleavage surface

1986 ◽  
Vol 44 ◽  
pp. 382-383
Author(s):  
H.-J. Ou
Keyword(s):  
Electron Microscopy ◽  
Small Particle ◽  
Small Particles ◽  
Cleavage Surface ◽  
Metallic Particles ◽  
Microscopy Technique ◽  
Ceramic Surfaces ◽  
Reflection Electron Microscopy ◽  
New Perspective

The understanding of the interactions between the small metallic particles and ceramic surfaces has been studied by many catalyst scientists. We had developed Scanning Reflection Electron Microscopy technique to study surface structure of MgO hulk cleaved surface and the interaction with the small particle of metals. Resolutions of 10Å has shown the periodic array of surface atomic steps on MgO. The SREM observation of the interaction between the metallic particles and the surface may provide a new perspective on such processes.

Articulation Training: A New Perspective

1979 ◽  
Vol 10 (3) ◽  
pp. 145-151 ◽  
Author(s):  
Sallie W. Hillard ◽  
Laura P. Goepfert
Keyword(s):  
Life Experience ◽  
Remediation Measures ◽  
New Perspective

This paper describes the concept of teaching articulation through words which have inherent meaning to a child’s life experience, such as a semantically potent word approach. The approach was used with six children. Comparison of pre/post remediation measures indicated that it has promise as a technique for facilitating increased correct phoneme production.

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