**A square matrix in which every element except the principal diagonal elements is zero** is called a Diagonal Matrix.

Diagonal Matrix:

A square matrix all of whose elements except those in the leading diagonal, are zero is called a diagonal matrix. For a square matrix A = [a_{ij}]_{n}_{xn}to be a diagonal matrix, a_{ij}= 0, whenever i not equal to j.

Any given square Matrix where all the elements are zero except for the elements that are present Diagonally is called a Diagonal Matrix. Let's assume a square Matrix [Aij]n x m can be called as a Diagonal Matrix if Aij= 0, if and only if i ≠ j. That is the Diagonal Matrix definition.

A diagonal matrix matrix is a special kind of symmetric matrix. It is a symmetric matrix with zeros in the off-diagonal elements.

A square matrix in which every element except the principal diagonal elements is zero is called a Diagonal Matrix. A square matrix D = [d

_{ij}]_{n x n}will be called a diagonal matrix if d_{ij}= 0, whenever i is not equal to j.

In Mathematics, a diagonal is a line that connects two vertices of a polygon or a solid, whose vertices are not on the same edge. In general, a diagonal is defined as a sloping line or the slant line, that connects to vertices of a shape. Diagonals are defined as lateral shapes that have sides/edges and corners.

The elements which do not lie on the leading diagonal of a square matrix is called non-diagonal elements of the matrix. Non-diagonal elements in a matrix. The number of rows is equal to the number of columns in a square matrix.

A zero square matrix is lower triangular, upper triangular, and also diagonal.

Diagonal matrices are both upper and lower triangular since they have zeroes above and below the main diagonal. The inverse of a lower triangular matrix is also lower triangular. The product of two or more lower triangular matrices is also lower triangular.

You can use the Pythagorean theorem to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w² , and now you should know how to find the diagonal of a rectangle explicit formula - just take a square root: d = √(l² + w²) .

Properties of a Diagonal Matrix

Every diagonal matrix is a square matrix. Identity matrix, null matrix, and scalar matrix are examples of a diagonal matrix as each of them has its non-principal diagonal elements to be zeros. The sum of two diagonal matrices is a diagonal matrix.

A diagonal matrix is defined as a square matrix in which all off-diagonal entries are zero. (Note that a diagonal matrix is necessarily symmetric.) Entries on the main diagonal may or may not be zero. If all entries on the main diagonal are equal scalars, then the diagonal matrix is called a scalar matrix.

Every diagonal matrix is orthogonal.

The only difference between the scalar matrix and a diagonal matrix is the elements of the principal diagonal. In a scalar matrix, the elements of the principal diagonal are all equal to the same constant value, and in a diagonal matrix the principal diagonal elements are all of different values.

As in other square matrices, there are two, but only one is important - the diagonal stretching from top left to bottom right.

In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of matrices, and is denoted by the symbol or followed by subscripts corresponding to the dimension of the matrix as the context sees fit.

In geometry, a diagonal is a straight line that joins two opposite corners in a flat four-sided shape such as a square.

The true statement is: a diagonal matrix is invertible if and only if its eigenvalues are nonzero.

The definition of diagonal is something with slanted lines or a line that connects one corner with the corner furthest away. An example of diagonal is a line going from the bottom left corner of a square to the top right corner.

When a square is circumscribed by a circle , the diagonal of the square is equal to the diameter of the circle.

A matrix that is both upper and lower triangular is diagonal. Matrices that are similar to triangular matrices are called triangularisable. A non-square (or sometimes any) matrix with zeros above (below) the diagonal is called a lower (upper) trapezoidal matrix. The non-zero entries form the shape of a trapezoid.

Matrix A is a diagonal matrix with a zero element in its diagonal. Therefore, matrix A is singular, and does not have an inverse.

The line stretching from one corner of the square or rectangle to the opposite corner through the centre of the figure is known as the diagonal. Any square that has two diagonals are equal in length to each other. Diagonal Formula is used to calculate the polygon diagonals.