# An Approach to Reduction of the Real Symmetric 3 x 3 Secular Problem and Applications

## Abstract

An original analytical method for casting a real three-dimensional symmetric matrix into its diagonal form along with explicit formulas for the corresponding eigenvectors is given. This is achieved by a two-step procedure relying on a nice geometrical parametrization of the rotational group SO(3) and the fundamental algebraic theorem about solutions of the polynomial equations.

- Authors:

- Institute of Biophysics, Bulgarian Academy of Sciences, Sofia (Bulgaria)
- Institute of Mechanics, Bulgarian Academy of Sciences, Sofia (Bulgaria)

- Publication Date:

- OSTI Identifier:
- 20692910

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Atomic Nuclei; Journal Volume: 68; Journal Issue: 11; Other Information: Translated from Yadernaya Fizika, ISSN 0044-0027, 68, 1978-1983 (No. 11, 2005); DOI: 10.1134/1.2131119; (c) 2005 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA); TN:

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; EIGENFUNCTIONS; EIGENVALUES; EIGENVECTORS; FIELD EQUATIONS; GEOMETRY; MATHEMATICAL SOLUTIONS; POLYNOMIALS; SO-3 GROUPS; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Mladenov, I.M., and Mladenova, C.D..
```*An Approach to Reduction of the Real Symmetric 3 x 3 Secular Problem and Applications*. United States: N. p., 2005.
Web. doi:10.1134/1.2131119.

```
Mladenov, I.M., & Mladenova, C.D..
```*An Approach to Reduction of the Real Symmetric 3 x 3 Secular Problem and Applications*. United States. doi:10.1134/1.2131119.

```
Mladenov, I.M., and Mladenova, C.D.. Tue .
"An Approach to Reduction of the Real Symmetric 3 x 3 Secular Problem and Applications". United States.
doi:10.1134/1.2131119.
```

```
@article{osti_20692910,
```

title = {An Approach to Reduction of the Real Symmetric 3 x 3 Secular Problem and Applications},

author = {Mladenov, I.M. and Mladenova, C.D.},

abstractNote = {An original analytical method for casting a real three-dimensional symmetric matrix into its diagonal form along with explicit formulas for the corresponding eigenvectors is given. This is achieved by a two-step procedure relying on a nice geometrical parametrization of the rotational group SO(3) and the fundamental algebraic theorem about solutions of the polynomial equations.},

doi = {10.1134/1.2131119},

journal = {Physics of Atomic Nuclei},

number = 11,

volume = 68,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}

DOI: 10.1134/1.2131119

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