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Scalar matrix is a type of diagonal matrix that has all the elements same or equal. The elements that are present other than in the diagonal are zero. A scalar matrix has on-diagonal elements non-zero.
The scalar matrix is a square matrix having an equal number of rows and columns. An example of a scalar matrix is A = \( \begin{bmatrix}5&0&0\\0&5&0\\0&0&5\end{bmatrix}\) Why Is It called a Scalar Matrix? The scalar matrix is referred to by the name of scalar, as it is obtained by multiplying a scalar constant with the identity matrix.
Jun 2, 2024 · A scalar matrix is a square matrix in which all of the principal diagonal elements are equal and the remaining elements are zero. It is a special case of a diagonal matrix and can be obtained when an identity matrix is multiplied by a constant numeric value. The matrix given below is a scalar matrix of order “4 × 4.”.
A scalar matrix is a type of square matrix. Its off-diagonal entries are equal to $ 0 $, and the on-diagonal (principal diagonal) elements are all equal. This article will give you a better understanding of a scalar matrix, some examples, a few of its properties, and how to multiply a matrix by a scalar.
Jun 29, 2023 · Examples of Scalar Matrix. A scalar matrix is a square matrix where all the diagonal elements are equal to a constant value (known as the scalar), and all the other elements are zero. Here are some examples of scalar matrices: The \(2 \times 2\) scalar matrix with scalar value \(3\): \(\begin{bmatrix}3&0\\0&3\\\end{bmatrix}\).
A scalar matrix is an upper triangular matrix and lower triangular matrix at the same time. The identity matrix is a scalar matrix. Any scalar matrix can be obtained from the product of an identity matrix and a scalar number. The zero matrix is a scalar matrix as well.
A scalar matrix is both an upper triangular matrix and a lower triangular matrix. The product of an identity matrix with a scalar integer yield a scalar matrix. The zero matrix is also a scalar matrix.
