Math Doubts

Diagonal Matrix

A square matrix whose non-diagonal elements are zero, is called a diagonal matrix.

diagonal matrix
Diagonal matrix

Square matrices are appeared with zeros. In a special case, a square matrix contains zero as non-diagonal elements but it contains elements only on principal diagonal. Due to having elements on leading diagonal and having zeros as non-diagonal elements, the square matrix is recognized as a diagonal matrix.

M = e 1⁣1 0 0 0 0 e 2⁣2 0 0 0 0 e 3⁣3 0 0 0 0 e m⁣m

The matrix is having elements e1⁣1, e2⁣2, e3⁣3, em⁣m only on principal diagonal but observe the elements on non-diagonal areas. All are zero elements at non-diagonal areas. Therefore, this type of matrix is called a diagonal matrix. The diagonal elements can be either equal or unequal elements.

It is simply expressed as M = diag e 1⁣1, e 2⁣2, e 3⁣3, e n⁣n

Example

D is a square matrix of order 5×5. It is having 25 element in five rows and five columns.

D = 1 0 0 0 0 0 5 0 0 0 0 0 7 0 0 0 0 0 3 0 0 0 0 0 9

The matrix D is having two types of elements. One type of elements are nonzero elements and remaining all are zeros. Nonzero elements (1, 5, 7, 3 and 9) are placed on the leading diagonal and remaining non-diagonal elements are zeros. Therefore, the matrix D is known as a diagonal matrix.

The diagonal matrix D is written in simple form D = diag 1, 5, 7, 3, 9



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