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- Usage of the word orthogonal outside of mathematics
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 symbolize
- linear algebra - What is the difference between orthogonal and . . .
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?
- What is orthogonal transformation? - Mathematics Stack Exchange
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 (when a basis is given) Orthogonal matrices represent transformations that preserves length of vectors and all angles between vectors, and all transformations that preserve length and angles are orthogonal
- Eigenvectors of real symmetric matrices are orthogonal
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 diagonalizable, this set will be a basis (just count dimensions) The result you want now follows
- orthogonal vs orthonormal matrices - what are simplest possible . . .
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 terminology is unfortunate, but it is what it is
- Orthogonal planes in n-dimensions - Mathematics Stack Exchange
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 they share a common line, hence in the latter case two vectors can be chosen both from the shared line and these are not orthogonal
- Eigenvalues in orthogonal matrices - Mathematics Stack Exchange
Two is false The determinant is $\pm 1$, not the eigenvalues in general Take a rotation matrix for example
- Are all eigenvectors, of any matrix, always orthogonal?
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 distinct eigenvalues are always orthogonal
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