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A Toeplitz matrix is defined as a constant-diagonal matrix.

A circular matrix is defined as a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector.

I cannot think of an example where a matrix would be Toeplitz but non-circular.

What is the difference between a Toeplitz matrix and a circular matrix?

simplytheaverage
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1 Answers1

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$$\begin{bmatrix}1 & 2 \\ 0 & 1 \end{bmatrix}$$ is a Toeplitz matrix but it is not circular.

$$\begin{bmatrix}1 & 2 \\ 2 & 1 \end{bmatrix}$$ is a circular matrix.

Toeplitz matrix for a $2$ by $2$ matrix is of the form of $$\begin{bmatrix}a & b \\ c & a \end{bmatrix}$$ but a circular matrix require it to be of the form of $$\begin{bmatrix}a & b \\ b & a \end{bmatrix}$$

Siong Thye Goh
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