This is independent of the diagonal form chosen to compute it.

For S is a pure state if and only if its diagonal form has exactly one non-zero entry which is a 1.

Classification of all quadratic forms up to equivalence can thus be reduced to the case of diagonal forms.

Every nondegenerate quadratic form on a real vector space is equivalent to the standard diagonal form:

This treatment in 1967 includes in short order both the diagonal form and the form with sinh and cosh.

Its diagonal forms were a much-noted departure from the cubical massing of the International Style that prevailed at the time.

The minimum and maximum distances to the origin can be read off the equation in diagonal form.

When using corner transfer matrices to perform calculations, it is both analytically and numerically convenient to work with their diagonal forms instead.

He also showed how to solve systems of linear equations be reducing the matrix of their coefficents to diagonal form.

This result is equivalent to stating that normal matrices can be brought to diagonal form by a unitary similarity transformation: