The sum of squared dimensions of a finite group's pairwise nonequivalent complex representations is equal to cardinality of that group.
Euclidean geometry and other inner-product spaces
The
Pythagorean theorem says that the square on the hypotenuse of a right triangle is equal in area to the sum of the squares on the legs. The sum of squares is not factorable.
The
squared Euclidean distance between two points, equal to the sum of squares of the differences between their coordinates
Heron's formula for the area of a triangle can be re-written as using the sums of squares of a triangle's sides (and the sums of the squares of squares)
This
article includes a list of related items that share the same name (or similar names). If an
internal link incorrectly led you here, you may wish to change the link to point directly to the intended article.
The sum of squared dimensions of a finite group's pairwise nonequivalent complex representations is equal to cardinality of that group.
Euclidean geometry and other inner-product spaces
The
Pythagorean theorem says that the square on the hypotenuse of a right triangle is equal in area to the sum of the squares on the legs. The sum of squares is not factorable.
The
squared Euclidean distance between two points, equal to the sum of squares of the differences between their coordinates
Heron's formula for the area of a triangle can be re-written as using the sums of squares of a triangle's sides (and the sums of the squares of squares)
This
article includes a list of related items that share the same name (or similar names). If an
internal link incorrectly led you here, you may wish to change the link to point directly to the intended article.