Bisymmetric matrix
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
Definition
A bisymmetric matrix is a square matrix that satisfies the following equivalent conditions:
- It is both a symmetric matrix and a centrosymmetric matrix.
- It is both a symmetric matrix and a persymmetric matrix.
- It is both a centrosymmetric matrix and a persymmetric matrix.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| symmetric Toeplitz matrix | |FULL LIST, MORE INFO | |||
| scalar matrix | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| symmetric matrix | symmetric about the main diagonal (top left to bottom right), or, equal to its matrix transpose | |FULL LIST, MORE INFO | ||
| persymmetric matrix | symmetric about the antidiagonal (bottom left to top right), or, commutes with the exchange matrix | |FULL LIST, MORE INFO | ||
| centrosymmetric matrix | symmetric about the center point. Note that this definition, although typically used for square matrices, also makes sense for rectangulra matrices | |FULL LIST, MORE INFO |