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
How do you orthogonally diagonalize the matrix? The same way you orthogonally diagonalize any symmetric matrix: you find the eigenvalues, you find an orthonormal basis for each eigenspace, you use the vectors in the orthogonal bases as columns in the diagonalizing matrix