diagonal matrix

A special case is the power of a diagonal matrix A.

In this case, we cannot reduce C to a diagonal matrix of units, since evidently.

In the general case, let T be the subgroup of diagonal matrices.

We now establish an important property of diagonal matrices.

Where is a diagonal matrix sorted in increasing order.

A diagonal matrix is one whose off-diagonal entries are all zero.

Complex numbers are block diagonal matrices with two 2x2 blocks.

We write as a block diagonal matrix, plus a rank-1 correction:

D is a diagonal matrix related to nodes' degrees.

Note that the eigenvalues appear in the diagonal matrix.

For example, if then where is the diagonal matrix of the squares of the eigenvalues.

M is a diagonal matrix of the nodal masses.

If all entries outside the main diagonal are zero, A is called a diagonal matrix.

Let be another set of formal variables, and let be a diagonal matrix.

The diagonal matrix M contains the masses on the diagonal.

The product of two anti-diagonal matrices is a diagonal matrix.

Multiplication operators generalize the notion of operator given by a diagonal matrix.

Diagonal matrices occur in many areas of linear algebra.

In practice, one would not implement actual matrix multiplication, since diagonal matrices are involved.

These operators can be characterized as those that commute with diagonal matrices:

Choosing T as diagonal matrix leaves the structure of A invariant.

In this type of transformation the 3x3 matrix is a diagonal matrix.

The standard inner product on R is given in coordinates by the diagonal matrix:

The matrix and its inverse are diagonal matrices.

It is a square matrix of order n, and also a special kind of diagonal matrix.