# Sufficient Condition for Consistency of Infinite Systems

## Abstract

Based on the theory of double series, we obtain a sufficient condition for the existence of strictly partial solutions to infinite systems of linear algebraic equations. We prove series expansion theorems for infinite determinants of Gaussian infinite matrices. Examples of application of the proposed condition are given.

- Authors:

- Novosibirsk State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771407

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; GAUSS FUNCTION; MATHEMATICAL SOLUTIONS; MATRICES; SERIES EXPANSION

### Citation Formats

```
Fedorov, F. M., E-mail: foma-46@mail.ru.
```*Sufficient Condition for Consistency of Infinite Systems*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3724-1.

```
Fedorov, F. M., E-mail: foma-46@mail.ru.
```*Sufficient Condition for Consistency of Infinite Systems*. United States. doi:10.1007/S10958-018-3724-1.

```
Fedorov, F. M., E-mail: foma-46@mail.ru. Sun .
"Sufficient Condition for Consistency of Infinite Systems". United States. doi:10.1007/S10958-018-3724-1.
```

```
@article{osti_22771407,
```

title = {Sufficient Condition for Consistency of Infinite Systems},

author = {Fedorov, F. M., E-mail: foma-46@mail.ru},

abstractNote = {Based on the theory of double series, we obtain a sufficient condition for the existence of strictly partial solutions to infinite systems of linear algebraic equations. We prove series expansion theorems for infinite determinants of Gaussian infinite matrices. Examples of application of the proposed condition are given.},

doi = {10.1007/S10958-018-3724-1},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 230,

place = {United States},

year = {2018},

month = {4}

}

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