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
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
How to find the orthogonal complement of a given subspace? The orthogonal complement is the set of all vectors whose dot product with any vector in your subspace is 0 It's a fact that this is a subspace and it will also be complementary to your original subspace
Orthogonal and symmetric Matrices - Mathematics Stack Exchange Conversely, every diagonalizable matrix with eigenvalues contained in {+ 1, − 1} and orthogonal eigenspaces is of that form It follows that the set of your matrices is in bijection with the set of subspaces of Cn
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
What is orthogonal transformation? - Mathematics Stack Exchange The equation ATA = AAT says that A − 1 = AT 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 Examples are rotations