Timeline for Multivariate normal distribution and orthonormal transformation
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 20, 2022 at 16:28 | comment | added | Iosif Pinelis | @KConrad : This is a good point; "orthogonal matrix" is indeed an example of bad generally accepted terminology/notation. | |
| Nov 20, 2022 at 16:06 | comment | added | KConrad | While there is no such thing as an orthonormal matrix, a good argument can be made that the usual term “orthogonal matrix” was a mistake and it should have been “orthonormal matrix” all along, because a real $n\times n$ matrix is an orthogonal matrix exactly when its columns are an orthonormal basis of $\mathbf R^n$, not just an orthogonal basis. Serge Lang, in the 3rd edition of his Algebra, bemoaned the terminology “orthogonal matrix” because such matrices are not just ones with orthogonal columns: the columns must be orthogonal unit vectors. He suggested the term “real unitary matrix”. | |
| Nov 20, 2022 at 14:35 | comment | added | Satya Prakash | The pdf of $Y$ is $$f_{Y}(y) = \frac{1}{2\pi(det(A\Sigma A^T))^{(1/2)}}exp[-(1/2)(AX-A\mu)^T(A\Sigma A^T)]^{-1}(XA-A\mu) = \frac{1}{2\pi(det(\Sigma ))^{(1/2)}}exp[-(1/2)(X-\mu)^T(\Sigma)]^{-1}(X-\mu)$$. | |
| Nov 20, 2022 at 14:27 | vote | accept | Satya Prakash | ||
| Nov 20, 2022 at 14:15 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |