Feb 11, 2011 · I always found the use of orthogonal outside of mathematics to confuse conversation. You might imagine two orthogonal lines or topics intersecting perfecting and …

Aug 26, 2017 · Orthogonal is likely the more general term. For example I can define orthogonality for functions and then state that various sin () and cos () functions are orthogonal. An …

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 …

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?

Sets of vectors are orthogonal or orthonormal. There is no such thing as an orthonormal matrix. An orthogonal matrix is a square matrix whose columns (or rows) form an orthonormal basis. …

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 …

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, …

Two is false. The determinant is $\pm 1$, not the eigenvalues in general. Take a rotation matrix for example.

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)$.

Dec 12, 2014 · Here, the result follows from the definition of "mutually orthogonal". A set of vectors is said to be mutually orthogonal if the dot product of any pair of distinct vectors in the …