Orthonormal Columns Imply Orthonormal Rows Example 1

This example demonstrates the geometric phenomenon that if a set of column vectors in a matrix is orthonormal, then the corresponding row vectors of its transpose matrix are also orthonormal. Key mathematical concepts include vector spaces, orthogonality, normalization, matrix transpose, and linear algebra. The construction utilizes GeoGebra commands/objects such as a1, a2, a3, at1, at2, at3, u1, u2, u3, ut1, ut2, ut3, T. It is suitable for university-level linear algebra courses, helping students visualize and understand the properties of orthogonality in matrices, deepening their grasp of vector spaces and matrix operations.