This article defines a property that can be evaluated for a square matrix. In other words, given a square matrix (a matrix with an equal number of rows and columns) the matrix either satisfies or does not satisfy the property.
View other properties of square matrices
A scalar matrix can be defined in the following equivalent ways:
- It is a diagonal matrix where all the diagonal entries are equal to one another.
- It is a scalar multiple of the identity matrix.
Suppose is a positive integer. A matrix is termed a scalar matrix if both the following hold:
- Non-diagonal entries are zero:
- Diagonal entries are equal to one another:
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|diagonal matrix||all off-diagonal entries are zero, but the diagonal entries may differ from one another||The matrix is diagonal but not scalar.||||
|Toeplitz matrix||each row is obtained as a cyclic shift (by one to the right) of the preceding row||A matrix of the form||||
|symmetric matrix||equals its matrix tranpose||(via diagonal matrix)||(via diagonal matrix)||Bisymmetric matrix, Diagonal matrix|FULL LIST, MORE INFO|