Matrix Invertibility
https://www.maa.org/taxonomy/term/42299/all
enFinite Groups of 2 x 2 Integer Matrices
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/finite-groups-of-2-x-2-integer-matrices
<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 shows that a finite group \(G\) can be represented as a group of invertible \( 2 \times 2\) integer matrices if and only if \(G\) is isomorphic to a subgroup of the dihedral groups \(D_4\) or \(D_6\). Results are obtained by studying the relation between \(GL(2,\mathbf{Z})\) and \(SL(2,3)\).</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95415 at https://www.maa.orgDoes the Generalized Inverse of \(A\) Commute with \(A\)?
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/does-the-generalized-inverse-of-a-commute-with-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>Not all square matrices commute with their generalized inverse (Moore-Penrose inverse). The author gathers equivalent conditions for the generalized inverse of a matrix to commute with the matrix itself. Then he shows that, in this case, the generalized inverse may be represented as a polynomial in the given matrix.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95504 at https://www.maa.orgAn Alternate Proof of Cramer's Rule
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-alternate-proof-of-cramers-rule
<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 a short proof of Cramer’s rule that avoids using the adjoint of a matrix.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95777 at https://www.maa.orgGaussian Elimination in Integer Arithmetic: An Application of the \(L\)-\(U\) Factorization
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/gaussian-elimination-in-integer-arithmetic-an-application-of-the-l-u-factorization
<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>Using L-U factorization, the author generates examples of matrices for which Gaussian elimination process can be done in integer arithmetic, including examples of matrices that are invertible over the integers.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com94804 at https://www.maa.orgA Geometric Intrepretation of the Columns of the (Pseudo) Inverse of A
https://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>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com94806 at https://www.maa.orgImage Reconstruction in Linear Algebra
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/image-reconstruction-in-linear-algebra
<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 main object is to solve the inverse problem of recovering the original scene, represented by a vector or a matrix, from its photograph, represented by a product of a matrix and the original vector or matrix. The solution of the resulting matrix equation gives rise to the reconstruction of the original scene</em>.</p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95016 at https://www.maa.orgFinding a Determinant and Inverse Matrix by Bordering
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/finding-a-determinant-and-inverse-matrix-by-bordering
<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 authors present a procedure for finding the determinant and inverse of a special class of matrices. The strategy adds borders to the original matrix, and makes use of row operations and determinant rules.</em></p>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95091 at https://www.maa.orgA Picture is Worth a Thousand Words
https://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>
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Fri, 12 Jul 2013 15:03:25 +0000
hosted@newtarget.com95111 at https://www.maa.orgA fresh approach to the singular value decomposition
https://www.maa.org/programs/faculty-and-departments/course-communities/a-fresh-approach-to-the-singular-value-decomposition
Tue, 15 Apr 2014 02:11:56 +0000
lang382674 at https://www.maa.orgFull Rank Factorization of Matrices
https://www.maa.org/programs/faculty-and-departments/course-communities/full-rank-factorization-of-matrices
Tue, 15 Apr 2014 20:00:04 +0000
lang383057 at https://www.maa.orgInverse Matrix Calculator
https://www.maa.org/programs/faculty-and-departments/course-communities/inverse-matrix-calculator
Tue, 15 Apr 2014 20:12:13 +0000
lang383058 at https://www.maa.orgMatrix Inverse Applet
https://www.maa.org/programs/faculty-and-departments/course-communities/matrix-inverse-applet
Wed, 23 Apr 2014 16:21:56 +0000
lang387684 at https://www.maa.orgOnline Math Lab at UC Santa Barbara
https://www.maa.org/programs/faculty-and-departments/course-communities/online-math-lab-at-uc-santa-barbara
Thu, 24 Apr 2014 16:15:16 +0000
lang388332 at https://www.maa.orgPseudoinverse
https://www.maa.org/programs/faculty-and-departments/course-communities/pseudoinverse
Fri, 25 Apr 2014 02:09:55 +0000
lang388838 at https://www.maa.orgThe Inverse
https://www.maa.org/programs/faculty-and-departments/course-communities/the-inverse
Fri, 25 Apr 2014 20:04:11 +0000
lang389310 at https://www.maa.org