Orthogonal & Symmetric Matrices
For a matrix A to be orthogonal, its column vectors must be an orthonormal basis. Is this correct? The textbook also mentions that length/magnitude of and angles between (including the 90degree angle) vectors multiplied times A are both preserved. Aside from these, are there any other important properties of orthogonal matrices that we should be aware of? Additionally, a symmetric matrix, which is something completely different (meaning that A = $A^{T}$), doesn't necessarily have to be orthogonal. What are the key properties of symmetric matrices?
haochiencho: June 5, 2015, 5:22 p.m.
Yes, an orthogonal matrix must have column vectors that form an orthonormal basis by definition. This also means that $Q^T=Q (inverse)$ .