Some Innovations in the Linear Algebra Course

Some Innovations in the Linear Algebra Course

The article proposes a number of innovations in the linear algebra course. A simple and convenient rule for implementing Gaussian elimination when transforming a matrix is proposed. Further, in the construction of the course, matrices with vector elements are systematically used, when presenting the...

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Bibliographic Details
Published in:2024 4th International Conference on Technology Enhanced Learning in Higher Education (TELE) pp. 162 - 165
Main Authors: Vybornov, Alexander N., Rusakov, Alexander A.
Format: Conference Proceeding
Language:English
Published: IEEE 20-06-2024
Subjects:
Coherence
Education
Eigenvalues and eigenfunctions
linear algebra
matrices
Symmetric matrices
Task analysis
teaching methodology
teaching methods in higher education
Technological innovation
Vectors
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Summary:The article proposes a number of innovations in the linear algebra course. A simple and convenient rule for implementing Gaussian elimination when transforming a matrix is proposed. Further, in the construction of the course, matrices with vector elements are systematically used, when presenting the theory of bilinear functions, the bilinear function is treated as a binary operation on vectors (with the appropriate notation), the operation extends (like a multiplication) to matrices with vector elements, all this makes the formulations and proofs of the theorems concise and clear. The paper also offers a concise and elegant proof of the theorem that all eigenvalues of a symmetric matrix are real numbers.
DOI:10.1109/TELE62556.2024.10605710