An orthogonal matrix is a square matrix whose rows and columns are orthogonal unit vectors. This means that when you multiply the matrix by its transpose, the result is the identity matrix. In mathematical terms, if A is an orthogonal matrix, then A^T A = I , where A^T is the transpose of A and I is the identity matrix. Orthogonal matrices preserve the length of vectors during transformations, making them useful in various applications, including computer graphics and signal processing. They are also closely related to concepts in linear algebra and rotation in Euclidean space.