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 deriving meaning from …

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 orthogonal basis …

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 being …

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. The …

Mar 17, 2017 · An orthogonal matrix can therefore be thought of as any "coordinate transformation" from your usual orthonormal basis $\ {\hat e_i\}$ to some new orthonormal basis $\ {\hat v_i\}.$ You can …

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, since symmetric …

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 corresponding to …

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

The important thing about orthogonal vectors is that a set of orthogonal vectors of cardinality (number of elements of a set) equal to dimension of space is guaranteed to span the space and be linearly …