An orthogonal matrix is a square matrix whose rows and columns are orthonormal vectors. This means that each row and each column has a length of one, and they are all perpendicular to each other. When an orthogonal matrix is multiplied by its transpose, the result is the identity matrix, which indicates that the original matrix preserves angles and lengths during transformations. Orthogonal matrices are important in various fields, including computer graphics, machine learning, and signal processing. They are used to perform rotations and reflections without distortion, making them valuable for maintaining the integrity of data and geometric shapes in calculations.