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Found total 224 results. Displaying results from 221 to 224.

 
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221
Compuatation of some determinants
Linear Algebra

The purpose of this article is to highlight how the characterizing properties of determinants allow us to compute the determinants. Though the determinants are defined using normalization, mutli-linearity and skew-symmetry, students are not exposed to the utility of this definition in the computation of the determinants. We give a few examples to show how the abstract definition coupled/combined with Laplace expansion makes the computations easier.

Keywords : Determinants, Multilinearity, Laplace expansions

BSc, MSc
MTTS Level :
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(Downloaded 134 times last on 22 December 2024, 01:23 pm
222
How to create new inner products on R^2?
Linear Algebra

We show by elementary means how to construct all inner products o R^2.

Keywords : Inner product, positive definite, Hessian

Final BSc, MSC
MTTS Level :
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(Downloaded 149 times last on 20 December 2024, 03:30 am
223
Polynomials with Integrer Coefficients
Ring Theory, Field Theory, Modern Algebra

Non-constant $f(X)in Z[X]$ has Zeros in $Z_p$ for Infinitely Many Primes $p$

Keywords : Polynomials, Roots, zeros, modulo a prime

MSc
MTTS Level : 2
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(Downloaded 138 times last on 19 December 2024, 09:30 pm
224
Transfer of Mathematical Structures
General

Let $fcolon Xto Y$ be a bijection. Assume that one of $X$ and $Y$ has a mathematical structure (for example, it may be a group structure, vector space structure, metric space structure or a topology). Then we may use $f$ to transfer the structure to the other set. We explain this construction with examples and bring out the significance of ``isomorphisms" and demystify the way some esoteric examples are constructed.

Keywords : Isomorphisms

3rd BSc onward
MTTS Level :
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(Downloaded 88 times last on 19 December 2024, 09:30 pm