by

Ciro Santilli (@cirosantilli, 37)

Symmetric matrix

A matrix that equals its transpose:

M = M^{T}

Can represent a symmetric bilinear form as shown at matrix representation of a symmetric bilinear form, or a quadratic form.

Table of contents
- Definite matrix Symmetric matrix
  - Positive definite matrix Definite matrix
- Skew-symmetric matrix Symmetric matrix
  - Skew-symmetric form Skew-symmetric matrix

Definite matrix

 1  0 

The definition implies that this is also a symmetric matrix.

Positive definite matrix

 0  0 

The dot product is a positive definite matrix, and so we see that those will have an important link to familiar geometry.

Skew-symmetric matrix (Antisymmetric matrix)

 1  0 

WTF is a skew? "Antisymmetric" is just such a better name! And it also appears in other definitions such as antisymmetric multilinear map.

Skew-symmetric form

 0  0 

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Symmetric matrix by

Wikipedia Bot 0  1970-01-01

A symmetric matrix is a square matrix that is equal to its transpose. In mathematical terms, a matrix \( A \) is considered symmetric if: \[ A = A^T \] where \( A^T \) denotes the transpose of the matrix \( A \).

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