A daughter gets an X chromosome from her mother and an X chromosome from her father. Suppose the X chromosome from her mother has the gene for normal blood clotting. Suppose the X chromosome from her father has the gene for hemophilia.
By Kardi Teknomo, PhD. A matrix is orthogonal if the transpose is equal to its inverse, that is. Since computing matrix inverse is rather difficult while computing matrix transpose is straightforward, orthogonal matrix make difficult operation easier. Orthogonal matrix is important in many applications because of its properties. Example:
A normal vector of a point on a smooth surface is any vector perpendicular to the (hyper)plane that best approximates the surface at that point. It is also common to require that normal vectors be unit-length and pointed 'outward' on a closed surface. A collection of vectors is orthogonal if and only if they are pairwise perpendicular. Expanding on this, a matrix is orthogonal iff its column vectors are orthogonal and unit length (this latter requirement has nothing to do with orthogonality, and the fact that such a matrix is called orthogonal instead of orthonormal is historical baggage).