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Results tagged with linear-algebra
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user 5371
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
12
votes
Accepted
Logarithm of a matrix
You may want to take a look at "Functions of Matrices: Theory and Computation" by Higham. Chapter 11 is specifically devoted to the matrix logarithm. In particular, the chapter contains a thorough co …
- 22.3k
17
votes
Does this formula have a rigorous meaning, or is it merely formal?
Back in the 19th century, when people had been experimenting with determinants a lot, they might have interpreted the above definition of $B\times C$ in terms of quaternions. If $i$, $j$, and $k$ deno …
- 22.3k
69
votes
Accepted
Determinant of sum of positive definite matrices
The inequality
$$\det(A+B)\geq \det A +\det B$$
is implied by the Minkowski determinant theorem
$$(\det(A+B))^{1/n}\geq (\det A)^{1/n}+(\det B)^{1/n}$$
which holds true for any non-negative $n\times …
- 22.3k