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Results tagged with linear-algebra
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user 6210
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
1
vote
How many parameters are needed to specify a k-dimensional subspace of R^d?
Here is a more geometric way to find the answer. We can specify a $k$ dimensional subspace by giving $k$ vectors in that subspace. That would require $kn$ parameters, but we are overspecifying. By how …
- 493
7
votes
1
answer
500
views
Numerical linear algebra: how to compute $b^TA^{-1}b$ efficiently
What is the most efficient way to compute $b^TA^{-1}b$ for a given $A$ and $b$?
Do we have to calculate $A^{-1}b$, or is this not necessary?
edit: I forgot to mention that A is symmetric and positiv …
- 493
23
votes
2
answers
2k
views
Formula expressing symmetric polynomials of eigenvalues as sum of determinants
The trace of a matrix is the sum of the eigenvalues and the determinant is the product of the eigenvalues. The fundamental theorem of symmetric polynomials says that we can write any symmetric polynom …
- 493