17 results about "Orthogonal matrix" patented technology

An orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e. QᵀQ=QQᵀ=I, where I is the identity matrix. This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse: Qᵀ=Q⁻¹. An orthogonal matrix Q is necessarily invertible (with inverse Q⁻¹ = Qᵀ), unitary (Q⁻¹ = Q∗) and therefore normal (Q∗Q = QQ∗) in the reals.