Connection To Principal Angles
Assuming that and have zero expected values, i.e., their covariance matrices and can be viewed as Gram matrices in an inner product, see Covariance#Relationship_to_inner_products, for the columns of and, correspondingly. The definition of the canonical variables and is equivalent to the definition of principal vectors for the pair of subspaces spanned by the columns of and with respect to this inner product. The canonical correlations is equal to the cosine of principal angles.
Read more about this topic: Canonical Correlation
Famous quotes containing the words connection to, connection and/or principal:
“It may comfort you to know that if your child reaches the age of eleven or twelve and you have a good bond or relationship, no matter how dramatic adolescence becomes, you children will probably turn out all right and want some form of connection to you in adulthood.”
—Charlotte Davis Kasl (20th century)
“We will have to give up the hope that, if we try hard, we somehow will always do right by our children. The connection is imperfect. We will sometimes do wrong.”
—Judith Viorst (20th century)
“The principal saloon was the Howlin’ Wilderness, an immense log cabin with a log fire always burning in the huge fireplace, where so many fights broke out that the common saying was, “We will have a man for breakfast tomorrow.””
—For the State of California, U.S. public relief program (1935-1943)