The Unapologetic Mathematician

Mathematics for the interested outsider

Matrices I

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May 20, 2008 - Posted by | Algebra, Linear Algebra


  1. […] Einstein Summation Convention Look at the formulas we were using yesterday. There’s a lot of summations in there, and a lot of big sigmas. Those get really tiring to […]

    Pingback by The Einstein Summation Convention « The Unapologetic Mathematician | May 21, 2008 | Reply

  2. […] Matrices II With the summation convention firmly in hand, we continue our discussion of matrices. […]

    Pingback by Matrices II « The Unapologetic Mathematician | May 22, 2008 | Reply

  3. […] compose two morphisms by the process of matrix multiplication. If is an matrix in and is a matrix in , then their product is a matrix in (remember the […]

    Pingback by The Category of Matrices I « The Unapologetic Mathematician | June 2, 2008 | Reply

  4. […] satisfies ), we construct the column vector (here ). But we’ve already established that matrix multiplication represents composition of linear transformations. Further, it’s straightforward to see that the linear transformation corresponding to a […]

    Pingback by The Category of Matrices III « The Unapologetic Mathematician | June 23, 2008 | Reply

  5. […] vector space comes equipped with a basis , where has a in the th place, and elsewhere. And so we can write any such transformation as an […]

    Pingback by The General Linear Groups « The Unapologetic Mathematician | October 20, 2008 | Reply

  6. […] Okay, back to linear algebra and inner product spaces. I want to look at the matrix of a linear map between finite-dimensional inner product […]

    Pingback by Matrix Elements « The Unapologetic Mathematician | May 29, 2009 | Reply

  7. […] the space of -tuples of complex numbers — and that linear transformations are described by matrices. Composition of transformations is reflected in matrix multiplication. That is, for every […]

    Pingback by Some Review « The Unapologetic Mathematician | September 8, 2010 | Reply

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