I'm trying to understand orthogonal and orthonormal matrices and I'm very confused. Unfortunately most sources I've found have unclear definitions, and many have conflicting …

Google searching reveals that "orthogonal validation" in an experimental context can mean different things in different fields. "Orthogonal" is often applied loosely to anything that …

Returns or evaluates orthogonal polynomials of degree 1 to degree over the specified set of points x. These are all orthogonal to the constant polynomial of degree 0.

Explore related questions orthogonal-polynomials See similar questions with these tags.

For fitting a line or hyperplane through points, principal component analysis is mathematically equivalent to total least squares. For details, see H. Späth: "Orthogonal least squares fitting …

Also, orthogonal set and linearly independent set both generate the same subspace. (Is that right?) Then orthogonal $\rightarrow$ linearly independent but orthogonal $\nleftarrow$ …

After the varimax rotation, the loading vectors are not orthogonal anymore (even though the rotation is called "orthogonal"), so one cannot simply compute orthogonal projections of the …

Nov 4, 2015 · To check whether two functions are orthogonal, you simply take their inner product in $\mathbb {R}^n$. That is, you multiply the functions on the subintervals and then sum the …

2) More importantly linear independent eigenvectors to the same eigenvalue do not need to be orthogonal. What is true however is that two eigenvectors to different eigenvalues of a …

Now find an orthonormal basis for each eigenspace; since the eigenspaces are mutually orthogonal, these vectors together give an orthonormal subset of $\mathbb {R}^n$. Finally, …