I always found the use of orthogonal outside of mathematics to confuse conversation. You might imagine two orthogonal lines or topics intersecting perfecting and deriving meaning from that …

Figure 22 (a) shows what A-orthogonal vectors look like. Imagine if this article were printed on bubble gum, and you grabbed Figure 22 (a) by the ends and stretched it until the ellipses …

An orthogonal projection is not what is represented by an orthogonal matrix. It just orthogonally projects the space onto some subspace. Since subspaces have lower dimension, they cannot …

I know that two functions are called orthogonal if at every point their tangents lines are perpendicular to each other. If I differentiate both of these functions, and the resulting …

Here are couple of my additions to Arturo's answer. Any symmetric matrix which can be diagonalized can be re-written in an orthogonal diagonalized form. Another aspects of this …

Dec 3, 2019 · Generally speaking, when you see the phrase “orthogonal projection matrix,” it means the latter: in other words, you should parse the phrase as “ (orthogonal projection) …

Aug 26, 2017 · It seems to me that perpendicular, orthogonal and normal are all equivalent in two and three dimensions. I'm curious as to which situations you would want to use one term over …

What does it mean for characters to be orthogonal? For example, if we take the following definition of the Orthogonality relation for characters: $$ \\sum_{r = …

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, …

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 …