Eigenvalues and Eigenvectors
https://maa.org/taxonomy/term/41374/all
enA Random Ladder Game: Permutations, Eigenvalues, and Convergence of Markov Chains
https://maa.org/programs/maa-awards/writing-awards/a-random-ladder-game-permutations-eigenvalues-and-convergence-of-markov-chains
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><b>Award:</b> George Pólya</p>
<p><b>Year of Award:</b> 1993</p>
<p><b>Publication Information:</b> <i>The</i> <i>College Mathematics Journal</i>, Vol. 23, No. 5, (1992), pp. 373-385</p>
<p><b>Summary:</b> A motivational setting for introducing students to important theorems of linear algebra.</p>
<p><a title="Read the Article" href="/sites/default/files/pdf/upload_library/22/Polya/07468342.di020754.02p0120e.pdf">Read the Article</a></p></div></div></div>Complex Eigenvalues and Rotations: Are Your Students Going in Circles?
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/complex-eigenvalues-and-rotations-are-your-students-going-in-circles
<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 shows that every \(2 \times 2\) real matrix with nonreal eigenvalues represents the composition of the following three operations: (1) a vertical “lift” to a plane through the origin, (2) a rotation in that plane, and (3) a “drop” back into the \(x-y\)-plane.</em></p>
</div></div></div>Clock Hands Pictures for \(2 \times 2\) Real Matrices
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/clock-hands-pictures-for-2-times-2-real-matrices
<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 article illustrates the notion of eigenvalue and its corresponding eigenvector using hands of an analog clock. This capsule deals with \(2 \times 2\) real matrices, single eigenvalues, and complex ones as well.</em></p>
</div></div></div>The Matrix of a Rotation
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-matrix-of-a-rotation
<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>Given a unit vector \(p\) in \( \mathbf{R}^3\) and an angle \( \theta\), what is the matrix of the rotation of \(\mathbf{R}^3\) about \(p\) through an angle of \(\theta\) in terms of the standard basis? The author obtains an explicit matrix without changing bases.</em></p>
</div></div></div>On the Convergence of the Sequence of Powers of a \(2 \times 2\) Matrix
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-convergence-of-the-sequence-of-powers-of-a-2-times-2-matrix
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The fact that the <em>limit of the \(n\)-th power of a \(2\times 2\) matrix \(A\) tends to \(0\) if \( \det A < 1\) and \( \mid 1 + \det(A) \mid > \mid\) tr\( (A) \mid \)</em> is used to prove a well-known theorem in Markov chains for \(2 \times 2\) regular stochastic matrices and to obtain an explicit formula for the stationary matrix and eigenvector.</p>
</div></div></div>Rank According to Perron: A New Insight
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/rank-according-to-perron-a-new-insight
<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>Suppose we have several alternatives that we wish to rank. For example, we may wish to rank five teachers according to their teaching excellence. The author constructs a positive matrix \(A\) based on pairwise comparisons of the alternatives, and uses the Perron principal eigenvector to find a ranking. The author employs dominance walks to obtain these results.</em></p>
</div></div></div>Eigen demo with sound
https://maa.org/programs/faculty-and-departments/course-communities/eigen-demo-with-sound
Matrix Algebra Demos
https://maa.org/programs/faculty-and-departments/course-communities/matrix-algebra-demos
A Constructive Approach to Singular Value Decomposition and Symmetric Schur Factorization
https://maa.org/programs/faculty-and-departments/course-communities/a-constructive-approach-to-singular-value-decomposition-and-symmetric-schur-factorization
Exploration of Special Matrices
https://maa.org/programs/faculty-and-departments/course-communities/exploration-of-special-matrices
The Inverse
https://maa.org/programs/faculty-and-departments/course-communities/the-inverse
Iterative Methods for Computing Eigenvalues and Eigenvectors
https://maa.org/programs/faculty-and-departments/course-communities/iterative-methods-for-computing-eigenvalues-and-eigenvectors
Reversal Matices
https://maa.org/programs/faculty-and-departments/course-communities/reversal-matices
Computing Eigenvalues Using the QR Algorithm
https://maa.org/programs/faculty-and-departments/course-communities/computing-eigenvalues-using-the-qr-algorithm
Eigenvectors in 2D
https://maa.org/programs/faculty-and-departments/course-communities/eigenvectors-in-2d