Main diagonal

Encyclopedia

In linear algebra

, the

The main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. For example, the following matrix has 1s down its main diagonal:

A square matrix like the above in which the entries outside the main diagonal are all zero is called a diagonal matrix

. The sum of the entries on the main diagonal of a square matrix is known as the trace of that matrix.

The main diagonal of a rectangular matrix is the diagonal which runs from the top left corner and steps down and right, until the right edge or the bottom edge is reached.

The diagonal of a square matrix from the top right to the bottom left corner is called

Linear algebra

Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...

, the

**main diagonal**(sometimes**leading diagonal**or**major diagonal**or**primary diagonal**or**principal diagonal**) of a matrix is the collection of entries where is equal to .The main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. For example, the following matrix has 1s down its main diagonal:

A square matrix like the above in which the entries outside the main diagonal are all zero is called a diagonal matrix

Diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. The diagonal entries themselves may or may not be zero...

. The sum of the entries on the main diagonal of a square matrix is known as the trace of that matrix.

The main diagonal of a rectangular matrix is the diagonal which runs from the top left corner and steps down and right, until the right edge or the bottom edge is reached.

The diagonal of a square matrix from the top right to the bottom left corner is called

**antidiagonal**,**counterdiagonal**,**secondary diagonal**, or**minor diagonal**.