Matrix Factorizations
https://www.maa.org/taxonomy/term/42308/0
enApproaches to the Formula for the \(n\)th Fibonacci Number
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/approaches-to-the-formula-for-the-nth-fibonacci-number
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>In this capsule, proofs of the equivalence of the two definitions of the Fibonacci numbers are discussed. This helps the undergraduate view mathematics as a unified whole with a variety of techniques.</em></p>
</div></div></div>Gaussian Elimination in Integer Arithmetic: An Application of the \(L\)-\(U\) Factorization
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/gaussian-elimination-in-integer-arithmetic-an-application-of-the-l-u-factorization
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Using L-U factorization, the author generates examples of matrices for which Gaussian elimination process can be done in integer arithmetic, including examples of matrices that are invertible over the integers.</em></p>
</div></div></div>Obtaining the \(QR\) Decomposition by Pairs of Row and Column Operations
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/obtaining-the-qr-decomposition-by-pairs-of-row-and-column-operations
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author gives an alternative to the usual Gram-Schmidt process and shows how to obtain the “QR Factorization” by using pairs of row column operations.</em></p>
</div></div></div>Using Quadratic Forms to Correct Orientation Errors in Tracking
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/using-quadratic-forms-to-correct-orientation-errors-in-tracking
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>If noise in data transmission produces a not quite orthogonal matrix that is known to be orthogonal, how does one find the "nearest" orthogonal matrix? This capsule recasts the problem as one of maximizing a quadratic form on the four-dimensional unit sphere, and sketches a solution.</em></p>
</div></div></div>A fresh approach to the singular value decomposition
https://www.maa.org/programs/faculty-and-departments/course-communities/a-fresh-approach-to-the-singular-value-decomposition
Full Rank Factorization of Matrices
https://www.maa.org/programs/faculty-and-departments/course-communities/full-rank-factorization-of-matrices
A Constructive Approach to Singular Value Decomposition and Symmetric Schur Factorization
https://www.maa.org/programs/faculty-and-departments/course-communities/a-constructive-approach-to-singular-value-decomposition-and-symmetric-schur-factorization
Online Matrix Calculator
https://www.maa.org/programs/faculty-and-departments/course-communities/online-matrix-calculator
Classroom Capsules and Notes for Matrix Factorizations in Linear Algebra
https://www.maa.org/programs/faculty-and-departments/course-communities/classroom-capsules-and-notes-for-matrix-factorizations-in-linear-algebra
Gram-Schmidt Orthogonalization:100 Years and More
https://www.maa.org/programs/faculty-and-departments/course-communities/gram-schmidt-orthogonalization100-years-and-more