Inner Product Spaces
http://www.maa.org/taxonomy/term/42304/0
enThe Axis of a Rotation: Analysis, Algebra, Geometry
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-axis-of-a-rotation-analysis-algebra-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><em>Given any 3 by 3 rotation matrix \(A\) (i.e. orthogonal with determinant \(1\) and an arbitrary vector \(x\), the vector \( Ax +A^{T}x+[1−\)tr\((A)]x\) lies on the axis of rotation. The article provides three different approaches, requiring various levels of background knowledge, to prove and/or explain the given result.</em></p>
</div></div></div>A Surprise from Geometry
http://www.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>On the Measure of Solid Angles
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-measure-of-solid-angles
<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 revisits formulas of measuring solid angles that he could find only in centuries-old literature, and provides modern versions of the proofs.</em></p>
</div></div></div>Projections in real inner product spaces
http://www.maa.org/programs/faculty-and-departments/course-communities/projections-in-real-inner-product-spaces
The Gram-Schmidt Algorithm
http://www.maa.org/programs/faculty-and-departments/course-communities/the-gram-schmidt-algorithm
Curve fitting project
http://www.maa.org/programs/faculty-and-departments/course-communities/curve-fitting-project
Terence Tao's Applets
http://www.maa.org/programs/faculty-and-departments/course-communities/terence-taos-applets
An Elementary Treatment of General Inner Products
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-elementary-treatment-of-general-inner-products
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>A typical first course on linear algebra is usually restricted to vector spaces over the real numbers and the usual positive-definite inner product. Hence, the proof that \(\dim(\mathcal{S}) + \dim(\mathcal{S^\perp}) = \dim(\mathcal{V})\) is not presented in a way that generalizes to non-positive-definite inner products or to vector spaces over other fields. In this note the author gives such a proof.</p>
</div></div></div>Classroom Capsules and Notes for The link below takes you to the list of capsules in the subcategory Inner Product Spaces in Linear Algebra
http://www.maa.org/programs/faculty-and-departments/course-communities/classroom-capsules-and-notes-for-the-link-below-takes-you-to-the-list-of-capsules-in-the-subcategory