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 …

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 being …

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 …

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 expressions are reciprocals of …

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 …

Now find an orthonormal basis for each eigenspace; since the eigenspaces are mutually orthogonal, these vectors together give an orthonormal subset of Rn R n. Finally, since symmetric matrices are …

Mar 17, 2017 · The equation ATA = AAT A T A = A A T says that A−1 =AT A 1 = A T so, at least, orthogonal matrices are easy to invert. What does it mean? Matrices represents linear transformation …

Sep 29, 2019 · The word "orthogonal" really just corresponds to the intuitive notion of vectors being perpendicular to each other. Draw out the unit vectors in the x x, y y and z z directions respectively- …