Eigenvalues and Eigenvectors
https://www.maa.org/taxonomy/term/41374/all
enA Random Ladder Game: Permutations, Eigenvalues, and Convergence of Markov Chains
https://www.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>
Thu, 17 Jul 2008 16:43:47 +0000
saratt113691 at https://www.maa.orgThe Matrix of a Rotation
https://www.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>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95128 at https://www.maa.orgOn the Convergence of the Sequence of Powers of a \(2 \times 2\) Matrix
https://www.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>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95406 at https://www.maa.orgRank According to Perron: A New Insight
https://www.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>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95470 at https://www.maa.orgComplex Eigenvalues and Rotations: Are Your Students Going in Circles?
https://www.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>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com94942 at https://www.maa.orgClock Hands Pictures for \(2 \times 2\) Real Matrices
https://www.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>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95100 at https://www.maa.orgEigen demo with sound
https://www.maa.org/programs/faculty-and-departments/course-communities/eigen-demo-with-sound
Thu, 24 Apr 2014 16:24:51 +0000
lang388333 at https://www.maa.orgMatrix Algebra Demos
https://www.maa.org/programs/faculty-and-departments/course-communities/matrix-algebra-demos
Fri, 25 Apr 2014 16:34:26 +0000
lang389179 at https://www.maa.orgA 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
Fri, 25 Apr 2014 16:51:38 +0000
lang389195 at https://www.maa.orgExploration of Special Matrices
https://www.maa.org/programs/faculty-and-departments/course-communities/exploration-of-special-matrices
Fri, 25 Apr 2014 17:00:40 +0000
lang389196 at https://www.maa.orgThe Inverse
https://www.maa.org/programs/faculty-and-departments/course-communities/the-inverse
Fri, 25 Apr 2014 20:04:11 +0000
lang389310 at https://www.maa.orgIterative Methods for Computing Eigenvalues and Eigenvectors
https://www.maa.org/programs/faculty-and-departments/course-communities/iterative-methods-for-computing-eigenvalues-and-eigenvectors
Fri, 25 Apr 2014 20:16:10 +0000
lang389331 at https://www.maa.orgReversal Matices
https://www.maa.org/programs/faculty-and-departments/course-communities/reversal-matices
Sat, 26 Apr 2014 00:10:40 +0000
lang389424 at https://www.maa.orgComputing Eigenvalues Using the QR Algorithm
https://www.maa.org/programs/faculty-and-departments/course-communities/computing-eigenvalues-using-the-qr-algorithm
Mon, 05 May 2014 15:19:21 +0000
lang397322 at https://www.maa.orgEigenvectors in 2D
https://www.maa.org/programs/faculty-and-departments/course-communities/eigenvectors-in-2d
Mon, 05 May 2014 15:41:08 +0000
lang397328 at https://www.maa.org