# Tagged Questions

Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level ...

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### Geometric Interpretation of Trace

This afternoon I was speaking with some graduate students in the department and we came to the following quandry; Is there a geometric interpretation of the trace of a matrix? This question ...
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### Geometric interpretation of characteristic polynomial

The coefficients of lowest and next-highest degree of a linear operator's characteristic polynomial are its determinant and trace. These have well-known geometric interpretations. But what about its ...
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### Eigenvalues of Matrix Sums

Is there a relationship between the eigenvalues of individual matrices and the eigenvalues of their sum? What about the special case when they are Hermitian and positive-definite? I am investigating ...
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### How fast can we *really* multiply matrices?

Background: The Strassen Algorithm, described here, has a computational complexity of $\text{O}(n^{2.807})$ for the multiplication of two $n \times n$ matrices (the exponent is $\frac{\log7}{\log2}$). ...
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### When to pick a basis?

Picking a specific basis is often looked upon with disdain when making statements that are about basis independent quantities. For example, one might define the trace of a matrix to be the sum of the ...
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