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QR Decomposition for the Least Squares Method: Theory and Practice
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Alexey L. Voskov – International Journal of Mathematical Education in Science and Technology, 2024
QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…
Descriptors: Mathematics, Algorithms, Data Science, Mathematical Concepts
A Note on Matrix Multiplication Appearing as Element Concatenation or Coinciding with Matrix Addition
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Samuel B. Allan; Peter K. Dunn; Robert G. McDougall – International Journal of Mathematical Education in Science and Technology, 2024
In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…
Descriptors: Mathematics Instruction, Teaching Methods, Multiplication, Addition
Euclid, Fibonacci, and Pascal--Recursed!
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Peelle, Howard A. – International Journal of Mathematical Education in Science and Technology, 1975
Use of the computer programs provided here in APL programming language can help students understand computational algorithms. (SD)
Descriptors: Algebra, Algorithms, College Mathematics, Computer Programs