# The Unapologetic Mathematician

## Matrices I

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 […]

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

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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 […]

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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 […]

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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 […]

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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 […]

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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 […]

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