Download An Introduction to Wavelets Through Linear Algebra by Michael W. Frazier PDF

By Michael W. Frazier

This article was once initially written for a "Capstone" direction at Michigan country college. A Capstone direction is meant for undergraduate arithmetic majors, as one of many ultimate classes taken of their undergraduate curriculum. Its objective is to assemble diversified themes coated within the undergraduate curriculum and introduce scholars to present advancements in arithmetic and their purposes. uncomplicated wavelet idea appears an ideal subject for any such path. As a subject matter, it dates again merely to 1985. in view that then there was an explosion of wavelet examine, either natural and utilized. Wavelet conception is at the boundary among arithmetic and engineering. particularly it's a reliable subject for demonstrating to scholars that arithmetic learn is prospering within the modern-day: scholars can see non-trivial arithmetic rules resulting in normal and critical purposes, comparable to video compression and the numerical answer of differential equations. the one must haves assumed are a uncomplicated linear algebra history and a little research historical past. this article is meant to be as common an advent to wavelet thought as attainable. it's not meant as a radical or authoritative reference on wavelet idea.

Show description

Read or Download An Introduction to Wavelets Through Linear Algebra (Undergraduate Texts in Mathematics) PDF

Best textbook books

Classical Mechanics

John Taylor has delivered to his new ebook, Classical Mechanics, all the readability and perception that made his advent to errors research a best-selling textual content. Classical Mechanics is meant for college kids who've studied a few mechanics in an introductory physics path, equivalent to "freshman physics.

Archaeology: Down to Earth

This new short version pairs of archaeology's so much well-known names -- David Hurst Thomas of the yank Museum of average background and Robert L. Kelly of the college of Wyoming. Their well-chosen examples exhibit how archaeologists have labored via real difficulties within the box and within the lab.

Exploring Art: A Global, Thematic Approach (4th Edition)

EXPLORING artwork makes use of artwork examples from worldwide to debate paintings within the context of faith, politics, relatives constitution, sexuality, leisure and visible tradition.

Counseling Research: Quantitative, Qualitative, and Mixed Methods

<P style="MARGIN: 0px">Using Counseling study: Quantitative, Qualitative, and combined equipment, counseling scholars are given the chance to profit examine layout, technique, and research via a counseling-specific framework. whereas different similar survey books on education-related examine and information don't comprise many particular examples and functions of quantitative, qualitative, and combined tools from the counseling career, this texts provides counseling scholars the chance to profit examine tools inside of their very own particular self-discipline.

Additional resources for An Introduction to Wavelets Through Linear Algebra (Undergraduate Texts in Mathematics)

Sample text

Ii. For j as in part i, prove that span{v1 , v2 , . . , vj , . . , vn } span{v1 , v2 , . . , vj−1 , vj+1 , . . , vn }. 9. Suppose u, v1 , v2 , . . , vn are vectors in some vector space. i. If u ∈ span {v1 , v2 , . . , vn }, prove that u, v1 , v2 , . . , vn are linearly dependent. ii. Suppose v1 , v2 , . . , vn are linearly independent. If u, v1 , v2 , . . , vn are linearly dependent, prove that u ∈ span{v1 , v2 , . . , vn }. 10. Suppose V is an n-dimensional vector space, k ≤ n, and {v1 , v2 , .

The span of U (denoted span U) is the set of all linear combinations of elements of U. In particular, if U is a finite set, say U {u1 , u2 , . . un }, then span U n j 1 αj uj : αj ∈ F for all j 1, 2, . . , n . 3. Vector Spaces and Bases 33 To visualize the span, note that the span of a single nonzero vector u in Rn consists of all vectors lying on the line through the origin that contains u. If u and v are two noncollinear vectors in R3 , then span {u, v} is the plane through the origin containing u and v.

I. (Factor theorem) Let P be a polynomial and let a ∈ C. We say z − a divides P, or z − a is a factor of P (written (z − a)|P), if there exists a polynomial Q such that P(z) (z − a)Q (z). Prove that (z − a)|P if and only if P(a) 0; that is, z − a is a factor of P if and only if a is a root of P. Hint: The “only if” direction is immediate. For the “if” direction, the result follows easily from the division algorithm for polynomials, if you are familiar with that. If not, a more elementary proof can be obtained by first showing that (z − a)|(z k − ak ) for any integer k ≥ 1.

Download PDF sample

Rated 4.40 of 5 – based on 11 votes