Null Matrix - Zero Matrix

Null Matrix is a matrix having zero as each of its elements. The null matrix is also called a zero matrix, and it can have different numbers of rows and columns. The addition of a null matrix to any matrix results in the same matrix, and hence a null matrix is also called the additive identity of the given matrix.

Let us learn more about the properties of the null matrix, with examples, FAQs.

Null matrix is a square matrix having zero as all its elements. Since the null matrix has all zeros as its elements, the null matrix is also referred to as a zero matrix. The null matrix is the additive identity of any matrix. The order of a null matrix is m x n, and it can have an unequal number of rows and columns. A few examples of zero matrix or null matrix is as follows.

\(\begin{bmatrix}0&0\\0&0\end{bmatrix}\)

\(\begin{bmatrix}0&0&0\\0&0&0\end{bmatrix}\)

\(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\)

The addition of zero matrix to any other matrix of the same order does not change the matrix and hence the null matrix is also called the additive identity.

\(\begin{bmatrix}a&b\\c&d\end{bmatrix}\) + \(\begin{bmatrix}0&0\\0&0\end{bmatrix}\) = \(\begin{bmatrix}a&b\\c&d\end{bmatrix}\)

The following are some of the important properties of the null matrix.

• The null matrix is a square matrix.
• The null matrix can have an unequal number of rows and columns.
• The addition of a null matrix to any matrix does not change the matrix.
• The multiplication of a null matrix with any other matrix changes the matrix into a null matrix.
• The determinant of a null matrix is equal to zero.
• The null matrix is a singular matrix.

Related Topics

The following topics help in a better understanding of null matrix.

• Idempotent Matrix
• Determinant Of Matrix
• Column Matrix
• Row Matrix

What Is Null Matrix?

The null matrix is a matrix having zero as all its elements. The null matrix is also called a zero matrix, as all its elements are zero. The addition of a null matrix to any matrix does not change the value of the matrix, and hence the null matrix is also called the additive identity.

Which Is The Difference Between Null Matrix And Zero Matrix?

The null matrix or a zero matrix refer to the same matrix, and both the matrices have zero as their elements.

What Is The Order Of Zero Matrix?

The order of a zero or null matrix is m x n and it can have different numbers of rows and columns. Hence a null matrix can be a square matrix or a rectangular matrix.

What Is The Use Of Null Matrix?

The null matrix is useful, as it is the additive identity of any matrix. The addition of a null matrix to any matrix does not change the value of the matrix, and hence the null matrix is also called the additive identity.