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>Thu, 17 Jul 2008 17:25:37 +0000saratt113701 at http://www.maa.orgTouching 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>Mon, 24 Aug 2009 13:11:55 +0000saratt113999 at http://www.maa.orgRoot 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>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95691 at http://www.maa.orgA 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>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95221 at http://www.maa.orgThe 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>Fri, 12 Jul 2013 15:03:25 +0000newton_admin95128 at http://www.maa.orgAdditivity + 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>Fri, 12 Jul 2013 15:03:25 +0000newton_admin94972 at http://www.maa.orgLinear Transformations in the Plane
http://www.maa.org/programs/faculty-and-departments/course-communities/linear-transformations-in-the-plane
Wed, 23 Apr 2014 16:49:40 +0000lang387714 at http://www.maa.orgChange of Basis
http://www.maa.org/programs/faculty-and-departments/course-communities/change-of-basis
Fri, 25 Apr 2014 01:40:03 +0000lang388766 at http://www.maa.orgComputer Graphics Project
http://www.maa.org/programs/faculty-and-departments/course-communities/computer-graphics-project
Fri, 25 Apr 2014 01:49:05 +0000lang388773 at http://www.maa.orgMatrix Algebra Demos
http://www.maa.org/programs/faculty-and-departments/course-communities/matrix-algebra-demos
Fri, 25 Apr 2014 16:34:26 +0000lang389179 at http://www.maa.orgLinear Algebra Toolkit
http://www.maa.org/programs/faculty-and-departments/course-communities/linear-algebra-toolkit-0
Fri, 25 Apr 2014 16:42:55 +0000lang389186 at http://www.maa.orgAnimating Transformations
http://www.maa.org/programs/faculty-and-departments/course-communities/animating-transformations
Sat, 26 Apr 2014 00:20:43 +0000lang389425 at http://www.maa.orgLinear 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
Mon, 05 May 2014 15:32:59 +0000lang397324 at http://www.maa.orgMatrix Transformations: "F"
http://www.maa.org/programs/faculty-and-departments/course-communities/matrix-transformations-f
Mon, 05 May 2014 15:48:18 +0000lang397329 at http://www.maa.orgLinear Transformation with Given Eigenvectors
http://www.maa.org/programs/faculty-and-departments/course-communities/linear-transformation-with-given-eigenvectors
Mon, 05 May 2014 15:54:07 +0000lang397330 at http://www.maa.org