minimal polynomial meaning in Hindi

Examples

1. The minimal polynomial for ( hence ) is a factor of.
2. Using the minimal polynomial of the next smallest Pisot Vijayaraghavan number gives,
3. Minimal polynomials are useful for constructing and analyzing field extensions.
4. In the second case, it follows that is the minimal polynomial of.
5. Minimal polynomials are also used to define conjugate elements.
6. Now we just need to find its minimal polynomial.
7. Therefore, is irreducible over by, and the minimal polynomial for is of degree.
8. While the Jordan normal form determines the minimal polynomial, the converse is not true.
9. The minimal polynomial is often the same as the characteristic polynomial, but not always.
10. Because has the same complex roots as the minimal polynomial and because it is real it follows that