Vector Spaces
https://maa.org/taxonomy/term/41379/all
enGenerating Exotic-Looking Vector Spaces
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/generating-exotic-looking-vector-spaces
<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>This note describes how to generate exercises allowing students to study nonstandard operations on familiar objects.</em></p>
</div></div></div>On Some Symmetric Sets of Unit Vectors
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-some-symmetric-sets-of-unit-vectors
<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 symmetric unit vectors \(u_i\), conditions on real numbers \(x_i\) are considered to be able to conclude that \(\sum x_i u_i \Rightarrow x_i = 0\) for all \(i\). Different kinds of “symmetry” lead to different conclusions.</em></p>
</div></div></div>A Surprise from Geometry
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-surprise-from-geometry
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Consider \(n\) vectors issuing from the origin in \(n\)-dimensional space. The author shows that the statement “any set of \(n\) vectors in \(n\)-space, no two of which meet at greater than right angles, can be rotated into the non-negative orthant” is true for \(n \leq 4\), but false for \(n>4\).</p>
</div></div></div>Change of Basis
https://maa.org/programs/faculty-and-departments/course-communities/change-of-basis
Matrix Algebra Demos
https://maa.org/programs/faculty-and-departments/course-communities/matrix-algebra-demos
Linear Algebra Toolkit
https://maa.org/programs/faculty-and-departments/course-communities/linear-algebra-toolkit-0
Bases of sums and intersections of subspaces
https://maa.org/programs/faculty-and-departments/course-communities/bases-of-sums-and-intersections-of-subspaces
Notes on left and right inverses
https://maa.org/programs/faculty-and-departments/course-communities/notes-on-left-and-right-inverses
Matrix Applet
https://maa.org/programs/faculty-and-departments/course-communities/matrix-applet-0
A Tricky Linear Algebra Example
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-tricky-linear-algebra-example
<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 article a classroom "trick" involving square arrangements of natural numbers is used to motivate a discussion of a special class of matrices. In particular, a basis is obtained for those \(n\) by \(n\) square matrices with the property that if \(n\) entries are selected from the matrix so that no two values are in the same row or the same column, then the sum of these \(n\) entries will always be the same.</em></p>
</div></div></div>Classroom Capsules and Notes for Vector Spaces, Subspaces in Linear Algebra
https://maa.org/programs/faculty-and-departments/course-communities/classroom-capsules-and-notes-for-vector-spaces-subspaces-in-linear-algebra
Transforming Linear Algebra Education with GeoGebra Applets
https://maa.org/programs/faculty-and-departments/course-communities/transforming-linear-algebra-education-with-geogebra-applets
A First Course in Linear Algebra
https://maa.org/programs/faculty-and-departments/course-communities/a-first-course-in-linear-algebra
Mathematical Treasure: Schlegel on Grassmanâ€™s Extension Theory
https://maa.org/press/periodicals/convergence/mathematical-treasure-schlegel-on-grassman-s-extension-theory
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Schlegel published Grassman's foundational work on vector spaces and linear algebra.</p>
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