The question of ‘what is scalar matrix’ is often asked among students studying matrices for the first time. Mathematics can be quite a difficult subject for a lot of students, but it can be understood through thorough thought though. So what is a scalar matrix?
A scalar matrix is a square matrix that has a constant value for all the elements of the principal diagonal, while the other elements of the matrix are zero. This is obtained when an identity matrix is multiplied by a numeric constant value. Another important property pertaining to scalar matrices is that a scalar matrix is always a square matrix.
To understand the concept of scalar matrices better, let us take a deep dive into it. Here are a few things to keep in mind when discussing scalar matrices.
An identity matrix is a square matrix that offers a multiplicative identity to matrices. The identity matrix has the number 1 as its diagonal element while all the other elements are zero. Identity matrices have several applications in the multiplication of matrices, as well as in finding the inverse of a matrix.
The diagonal matrix is also another square matrix, that has elements of different values across the principal diagonal while all other elements are zero. If the diagonal elements of the diagonal one are made equal, then it becomes a scalar matrix.
The principal diagonal in mathematics is the imaginary straight line that connects the elements of a diagonal matrix from the first element to the last one in a row or column. In the case of an identity matrix, the principal diagonal elements are all equal to one, while in the discussed matrix, they are all equal to a constant value like a whole number, real number, etc.