Orthonormal matrices

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors.... Wikipedia: Orthogonal matrix

The determinant of an orthonormal matrix is ​​equal to 1 or -1.

• det(Q) = 1 or -1

The inverse of an orthonormal matrix is ​​its transpose.

• QT = inv(Q)

The product the two orthonormal matrices is orthonormal.

• Q1 * Q2 = Q3

To solve an orthonormal system you can multiply the transpose of A by b. In fact, you are simply calculating the dot product of the rows of the transpose of A by the column b, instead of solving a linear system.

• Solve: Qx =b

• r_Q_mR();
• orth_mR(); Gram-Schmidt algorithm