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Chapter 3

Chapter 3

Chapter 3. L p -space. Preliminaries on measure and integration. ?-algebra. ? ?? is a set. ?is a family of subsets of ? with. ?is called ?-algebra of subsets of ?. measure space. ? ?? is a set. ?is a?-algebra of subsets of ?. ?:??[0, ?] satisfies .

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2.32k views • 209 slides
Chapter 3 Linear Algebra Review and Elementary Differential Equations

Chapter 3 Linear Algebra Review and Elementary Differential Equations

Chapter 3 Linear Algebra Review and Elementary Differential Equations To review some important concept of linear algebra and differential equations that will be used subsequently. Outline. Vector spaces and subspaces Independence, basis and dimension Norm and inner product

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1.19k views • 75 slides
Hodge Theory

Hodge Theory

Hodge Theory. Calculus on Smooth Manifolds. by William M. Faucette . Adapted from lectures by Mark Andrea A. Cataldo. Structure of Lecture. The Exterior Algebra The Star Isomorphism The Tangent and Cotangent Bundles The deRham Cohomology Groups Riemannian Metrics Partitions of Unity

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624 views • 62 slides
Preliminaries on normed vector space

Preliminaries on normed vector space

Preliminaries on normed vector space. E:normed vector space. :topological dual of E i.e. is the set of all continuous linear functionals on E. Continuous linear functional. :normed vector space. is a Banach space. Propositions about normed vector space.

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396 views • 27 slides
4.10 Inner Product Spaces

4.10 Inner Product Spaces

4.10 Inner Product Spaces. In this section, we extend those concepts of R n such as: dot product of two vectors, norm of a vector, angle between vectors, and distance between points, to general vector space.

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873 views • 20 slides
4.10 Inner Product Spaces

4.10 Inner Product Spaces

4.10 Inner Product Spaces. In this section, we extend those concepts of R n such as: dot product of two vectors, norm of a vector, angle between vectors, and distance between points, to general vector space.

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233 views • 20 slides
Linear algebra: matrix Eigen-value Problems

Linear algebra: matrix Eigen-value Problems

Linear algebra: matrix Eigen-value Problems. Eng. Hassan S. Migdadi. Part 3. Eigenvalue Problems. Eigenvalues and eigenvectors Vector spaces Linear transformations Matrix diagonalization. The Eigenvalue Problem. Consider a n x n matrix A Vector equation: Ax = l x

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842 views • 18 slides
II. Linear Geometry of n -Space

II. Linear Geometry of n -Space

II. Linear Geometry of n -Space. Vectors in Space Length and Angle Measures. II.1. Vectors in Space. See Apostol, Chap 1. Descartes: Points in plane ~ ( a 1 , a 2 ), points in space ~ ( a 1 , a 2 , a 3 ).

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278 views • 15 slides
Section 5.1

Section 5.1

Section 5.1. Real Vector Spaces. DEFINITION OF A VECTOR SPACE. Let V be any non-empty set of objects on which two operations are defined: addition and multiplication by scalars (numbers).

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208 views • 8 slides

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