2011年2月11日 · 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 …

2017年8月26日 · 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 …

2015年7月12日 · 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 …

2015年8月4日 · 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 …

2017年3月17日 · 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 …

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 …

3 Generally, two linear subspaces are considered orthogonal if every pair of vectors from them are perpendicular to each other. This doesn't wok in three dimensions: two planes are either parallel or …

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

2012年5月8日 · 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 …