Scalar matrix

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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


Verbal definition

A scalar matrix can be defined in the following equivalent ways:

Algebraic definition

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

Weaker 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