Main diagonal

Those elements are referred to as a diagonal in linear algebra, on an imaginary line which is inclined from top to bottom are located in a square matrix. Of particular importance is the main diagonal running from top left to bottom right.

Diagonal of a 2 × 2 matrix

In a matrix of the form

There are two diagonal: The items and form the main diagonal running from top left to bottom right. The entries and form the so-called secondary diagonal running from top right to bottom left.

The two diagonals of a matrix play an important role in the calculation of determinants: The following formula is

Which is often abbreviated linguistically imprecise to " determinant equal main diagonal minus secondary diagonal ".

The main diagonal of an n × n- matrix,

For a general matrix

With the entries of the main diagonal consists of the entries, so of all numbers that are on the line from top left to bottom right.

The term secondary diagonal matrices has in no uniform definition and can refer to a diagonal to the main diagonal above or below this parallel, or on the diagonal from top right to bottom left.

Comments

A square matrix in which only the elements on the main diagonal are different from zero, is a diagonal matrix. Do all these elements have the value 1, we obtain the so-called identity matrix.

The sum of the elements of the main diagonal is called the trace of the matrix.