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 …

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 …

Aug 4, 2015 · I am beginner to linear algebra. I want to know detailed explanation of what is the difference between these two and geometrically how these two are interpreted?

Jul 12, 2015 · I have often come across the concept of orthogonality and orthogonal functions e.g in fourier series the basis functions are cos and sine, and they are orthogonal. For vectors …

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 …

May 8, 2012 · In general, for any matrix, the eigenvectors are NOT always orthogonal. But for a special type of matrix, symmetric matrix, the eigenvalues are always real and eigenvectors …

Jul 28, 2017 · I wanted to find a direct equation for the orthogonal projection of a point (X,Y) onto a line (y=mx+b). I will refer to the point of projection as as $ (X_p,Y_p)$.

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, …

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 …

It is not reasonable to expect this as your property is invariant under an orthogonal change of basis. Thr characteristic polynomial is of degree 2 which tells you the eigenvalues, and since …