New answers tagged linear-algebra
3
votes
What does $(x_i - \xi_k)_+$ mean in this regression spline formula?
The second part of your question answers the first part. The + subscript says "Evaluate this and, if it is negative, substitute 0".
This is pretty common with splines, where effects are ...
- 111k
3
votes
Covariance matrix square root
The operator theorists sent me to talk to yall about Matrix Functions.
Given some analytic function $f$ defined on $\mathbb{R}$, we can extend its definition to square matrices by plugging a matrix ...
- 3,705
6
votes
Accepted
Covariance matrix square root
Every covariance matrix $\Sigma$ is positive semi-definite (PSD). Because $\Sigma$ is PSD, then there exists a unique PSD and symmetric matrix, let's call it $\Sigma^{1/2}$, such that $\Sigma = \Sigma^...
- 4,485
5
votes
Is the expectation of a random vector multiplied by its transpose equal to the product of the expectation of the vector and that of the transpose
Here's a discrete counter-example, if that's easier to wrap your head around.
Let
$$
\begin{align}
P(z_0=1 \wedge z_1=1) &= 0.5 \\
P(z_0=-1 \wedge z_1=-1) &= 0.5
\end{align}
$$
Then
$$
E[z] = ...
- 151
15
votes
Is the expectation of a random vector multiplied by its transpose equal to the product of the expectation of the vector and that of the transpose
To confirm a claim is not true, you don't "prove it". Instead, just provide a counterexample would be sufficient.
You are actually on the right track. Any random vector $z$ with positive ...
- 16.8k
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