Toplitz Theorem, namely Hellinger-Teplich Theorem and Mathematical Functional Analysis Theorem, is named after German mathematicians Ernst Herlinger and Otto Teplich.

Let h be a Hilbert space, and t: h → h be a symmetric linear operator defined everywhere, that is, for any

There are equations.

Then, t is bounded (and therefore continuous).

Extended data

Characteristics of elements of toplitz matrix

The matrix of 1 and Toplitz is completely determined by 2n-1 elements in its row 1 and column1. ?

2. The elements on each diagonal of 2.Toplitz matrix parallel to the main diagonal are equal and symmetrical about the cross diagonal. Obviously, there are:

In ...

Reverse identity matrix. ?

3. Except for the first row and the first column, all other elements are the same as those in the upper left corner.

4. Every element in the matrix is symmetric about the sub-diagonal, that is, the T-shaped matrix is a sub-symmetric matrix.

Special t-shaped matrix

In the field of digital signal processing, we often encounter a special T-matrix, which is not only characterized by a general T-matrix, but also a symmetric matrix.

Baidu Encyclopedia-Top Leeds Matrix

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