Orthogonality and Projections
http://www.maa.org/taxonomy/term/42301/0
enA Note on the Equality of the Column and Row Rank of a Matrix
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-note-on-the-equality-of-the-column-and-row-rank-of-a-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><em>An elementary argument, different from the usual one, is given for the familiar equality of row and column rank. The author takes “full advantage of the following two elementary observations: (1) For any vector \(x\) in \(\mathcal{R}^n\) and matrix \(A\), \(Ax\) is a linear combination of the columns of \(A\), and (2) vectors in the null space of \(A\) are orthogonal to vectors in the row space of \(A\), relative to the usual Euclidean product.”</em></p>
</div></div></div>A Picture is Worth a Thousand Words
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-picture-is-worth-a-thousand-words
<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 provides geometric illustrations of four subspaces associated with a matrix. Thinking of a matrix as a map between real vector spaces, the illustrations motivate the decomposition of the domain and range into orthogonal subspaces and the decomposition of vectors into orthogonal components. The author also indicates how the illustrations can be related to the solvability of certain matrix equations.</em></p>
</div></div></div>Obtaining the \(QR\) Decomposition by Pairs of Row and Column Operations
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/obtaining-the-qr-decomposition-by-pairs-of-row-and-column-operations
<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 gives an alternative to the usual Gram-Schmidt process and shows how to obtain the “QR Factorization” by using pairs of row column operations.</em></p>
</div></div></div>A Geometric Intrepretation of the Columns of the (Pseudo) Inverse of A
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-geometric-intrepretation-of-the-columns-of-the-pseudo-inverse-of-a
<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 pseudo inverse of a matrix \(A\) is used to obtain information about the rows of \(A\).</em></p>
</div></div></div>Full Rank Factorization of Matrices
http://www.maa.org/programs/faculty-and-departments/course-communities/full-rank-factorization-of-matrices
Online Math Lab at UC Santa Barbara
http://www.maa.org/programs/faculty-and-departments/course-communities/online-math-lab-at-uc-santa-barbara
Projections in real inner product spaces
http://www.maa.org/programs/faculty-and-departments/course-communities/projections-in-real-inner-product-spaces
Gram-Schmidt Calculator
http://www.maa.org/programs/faculty-and-departments/course-communities/gram-schmidt-calculator
The Gram-Schmidt Algorithm
http://www.maa.org/programs/faculty-and-departments/course-communities/the-gram-schmidt-algorithm
Gram-Schmidt Process in Three Dimensions
http://www.maa.org/programs/faculty-and-departments/course-communities/gram-schmidt-process-in-three-dimensions
Gram-Schmidt Process in Two Dimensions
http://www.maa.org/programs/faculty-and-departments/course-communities/gram-schmidt-process-in-two-dimensions
Computing Eigenvalues Using the QR Algorithm
http://www.maa.org/programs/faculty-and-departments/course-communities/computing-eigenvalues-using-the-qr-algorithm
Dot Product Applet
http://www.maa.org/programs/faculty-and-departments/course-communities/dot-product-applet
Terence Tao's Applets
http://www.maa.org/programs/faculty-and-departments/course-communities/terence-taos-applets
Classroom Capsules and Notes for Orthogonality and Projections in Linear Algebra
http://www.maa.org/programs/faculty-and-departments/course-communities/classroom-capsules-and-notes-for-orthogonality-and-projections-in-linear-algebra