Linear Algebra for Undergraduates.

Sage for Linear Algebra

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The Algebra of Linear Algebra

3. You are already familiar with the concept of vector spaces in the form of …nite dimensional Euclidean vector spaces, and most of what we do in these lectures will involve these spaces (and, indeed, will also assume that the dot product operation is well-de…ned so that we can de…ne the matrix operations associated with linear transformations). However, it will also be useful to consider some ...

Pharmacology – Prep Manual for Undergraduates

Templates for Linear Algebra ProblemsZhaojun

The increasing availability of advanced-architecture computers is having a very signiicant eeect on all spheres of scientiic computation, including algorithm research and software development in numerical linear algebra. Linear algebra {in particular, the solution of linear systems of equations and eigenvalue problems { lies at the heart of most calculations in scientiic computing. This chapter...

Formal Theories for Linear Algebra

We introduce two-sorted theories in the style of [CN10] for the complexity classes ⊕L and DET , whose complete problems include determinants over Z2 and Z, respectively. We then describe interpretations of Soltys’ linear algebra theory LAp over arbitrary integral domains, into each of our new theories. The result shows equivalences of standard theorems of linear algebra over Z2 and Z can be pro...