Linear Transformations
http://www.maa.org/taxonomy/term/41376/0
enOf Memories, Neurons, and Rank-One Corrections
http://www.maa.org/programs/maa-awards/writing-awards/of-memories-neurons-and-rank-one-corrections
<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> 1998</p>
<p><b>Publication Information:</b> <i>The</i> <i>College Mathematics Journal</i>, Vol. 27, No. 1, (1997), pp. 2-19</p>
<p><b>Summary:</b> A look at mnemonic techniques and neural networks through the construction of linear transformations by the accumulation of many small rank-one adjustments.</p>
<p><a title="Read the Article" href="/sites/default/files/pdf/upload_library/22/Polya/07468342.di020775.02p0278w.pdf">Read the Article</a></p></div></div></div>Touching the \(Z_2\) in Three-Dimensional Rotations
http://www.maa.org/programs/maa-awards/writing-awards/touching-the-z2-in-three-dimensional-rotations
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Award: </strong>Carl B. Allendoerfer</p>
<p><strong>Year of Award:</strong> 2009</p>
<p><strong>Publication Information:</strong><em>Mathematics Magazine</em>, vol. 81, no. 5, December 2008, pp. 345-357</p>
<p><strong>Summary:</strong> If we compose two nontrivial complete rotations, the resulting motion can always be deformed to the null motion. This paper gives a mathematical formulation of this non-obvious geometric property.</p></div></div></div>Root Preserving Transformations of Polynomials
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/root-preserving-transformations-of-polynomials
<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 answers negatively the question, “Is there a (non-trivial) linear transformation \(T\) from \(P_n\), the vector space of all polynomials of degree at most \(n\), to \(P_n\) such that for each \(p\) in \( P_n\) with a real or complex root, the polynomials \(p\) and \(T( p)\) have a common root?</em>" <em>The proof is based on the fact polynomials of degree at most \(n\) have at most \(n\) roots in the real or complex numbers. This article investigates an area common to algebra and linear algebra.</em></p>
</div></div></div>A Geometric Approach to Linear Functions
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-geometric-approach-to-linear-functions
<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>There are three somewhat distinct topics in this article: the condition for linear functions to commute, a linear function as a transformation of the number line, and linear difference equations. A linear function \(y=f(x)=ax+b\) can be characterized in terms of slope and the “center of reflection,” both of which reflect the geometric property of the function. </em></p>
</div></div></div>The Matrix of a Rotation
http://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>
</div></div></div>Additivity + Homogeneity
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/additivity-homogeneity
<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>Linear transformations satisfy properties of both additivity and homogeneity. This capsule presents classes of functions that satisfy additivity but not homogeneity and vice versa.</em></p>
</div></div></div>Linear Transformations in the Plane
http://www.maa.org/programs/faculty-and-departments/course-communities/linear-transformations-in-the-plane
Change of Basis
http://www.maa.org/programs/faculty-and-departments/course-communities/change-of-basis
Computer Graphics Project
http://www.maa.org/programs/faculty-and-departments/course-communities/computer-graphics-project
Matrix Algebra Demos
http://www.maa.org/programs/faculty-and-departments/course-communities/matrix-algebra-demos
Linear Algebra Toolkit
http://www.maa.org/programs/faculty-and-departments/course-communities/linear-algebra-toolkit-0
Animating Transformations
http://www.maa.org/programs/faculty-and-departments/course-communities/animating-transformations
Linear Transformation Given by Images of Basis Vectors
http://www.maa.org/programs/faculty-and-departments/course-communities/linear-transformation-given-by-images-of-basis-vectors
Matrix Transformations: "F"
http://www.maa.org/programs/faculty-and-departments/course-communities/matrix-transformations-f
Linear Transformation with Given Eigenvectors
http://www.maa.org/programs/faculty-and-departments/course-communities/linear-transformation-with-given-eigenvectors