Literature Notes
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<< /S /GoTo /D (subsection.0.17.1) >> /Resources 318 0 R 7 0 obj Linear algebra is one of the most applicable areas of mathematics. endobj 307 0 obj (Column Space) >> endobj << /S /GoTo /D (section.0.14) >> These linear algebra lecture notes are designed to be presented as twenty ve, fty minute lectures suitable for sophomores likely to use the material for applications but still requiring a solid foundation in this fundamental branch /MediaBox [0 0 595.276 841.89] << /S /GoTo /D (subsection.0.14.4) >> 304 0 obj endobj endobj Linear Algebra and Tensor Analysis Notes. << /S /GoTo /D (subsection.0.14.1) >>
<< /S /GoTo /D (subsection.0.8.2) >> Given two vector spaces V and W over a field F, a linear map (also called, in some contexts, linear transformation or linear mapping) is a map: → that is compatible with addition and scalar multiplication, that is (+) = + (), = ()for any vectors u,v in V and scalar a in F.
Algebra I. << /S /GoTo /D (subsection.0.5.3) >> 272 0 obj endobj Topics in our Linear Algebra and Tensor Analysis Notes PDF. /Font << /F43 5 0 R >>
NOTES ON LINEAR ALGEBRA LIVIU I. NICOLAESCU CONTENTS 1. 316 0 obj The determinant of a square matrix8 1.5. << /S /GoTo /D [317 0 R /Fit ] >> << /S /GoTo /D (part.4) >> (Transpose Review) Lecture 11. 8 0 obj endobj endobj << /S /GoTo /D (subsection.0.17.3) >> He received a B.S. endobj endobj 318 0 obj << endobj
endobj (Why Don't You have Multivariable Calculus Too?) endobj >> endobj 295 0 obj 259 0 obj 324 0 obj << endobj We use only one theoretical concept from linear algebra, linear independence, and only one computational tool, the QR factorization; our approach to most applica-tions relies on only one method, least squares (or some extension). endobj 280 0 obj
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<< /S /GoTo /D (section*.1) >> << /S /GoTo /D (section.0.6) >> It starts with solutions to systems of linear equations, like 3x +5y +7z = 8 x +y +z = 20; but also includes many operations from geometry such as rotations and re ections, and the structure of solutions to linear dierential equations. 131 0 obj 247 0 obj
(Exam Exercises) /Length 64 (Preface) %PDF-1.4 127 0 obj Symmetric and skew-symmetric forms7 1.4. (Diagonal Matrices) Looking for GATE Maths Notes Linear Algebra 2021? (Where Can I Give Feedback)
/Contents 3 0 R /ProcSet [ /PDF /Text ] (Other Resources) >> << /S /GoTo /D (subsection.0.14.5) >> (Exam Exercises) endobj (Exam Exercises) /Filter /FlateDecode All rights reserved. (Exam Exercises) 279 0 obj
<< /S /GoTo /D (section.0.1) >> << /S /GoTo /D (section.0.8) >> << /S /GoTo /D (subsection.0.12.1) >>
endobj << /S /GoTo /D (subsection.0.1.2) >> 288 0 obj endobj Removing #book# Additional properties of determinants.11 1.6. (Rotations) endobj << /S /GoTo /D (subsection.0.14.2) >> << /S /GoTo /D (part.3) >> 215 0 obj (Working with Respect to another Basis) (Composition and Matrix Multiplication) (Exam Exercises) << /S /GoTo /D (section.0.13) >> (Who This Book is For and What this Book is About) endobj 23 0 obj << /S /GoTo /D (subsection.0.9.1) >> endobj (Computing Determinants Quickly) 296 0 obj endobj
While there is some review of exponents, factoring and graphing it is assumed that not a lot of review will be needed to remind you how these topics work.Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.Here is a listing (and brief description) of the material that is in this set of notes.You appear to be on a device with a "narrow" screen width ( endobj (Dot and Cross Products) Mutilinear maps3 1.2. Are you sure you want to remove #bookConfirmation# endobj
endobj endobj 236 0 obj The basis and dimensions of matrix spaces. 68 0 obj
(A Very Important Tables) Exercises18 2. Multilinear forms and determinants3 1.1. << /S /GoTo /D (section.0.16) >> endobj (Matrix Vector Products) 67 0 obj 171 0 obj /MediaBox [0 0 595.276 841.89] 188 0 obj
endobj 115 0 obj 99 0 obj endobj 9 0 obj << 268 0 obj << /S /GoTo /D (section*.3) >> iv These lecture notes correspond to the course Linear Algebra II, as given at Queen Mary, University of London, in the first sememster 2005–6.
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endobj endobj (Quadratic Forms) endobj >> endobj << /S /GoTo /D (section.0.19) >> 32 0 obj endobj from your Reading List will also remove any endobj Included area a review of exponents, radicals, polynomials as well as indepth discussions of solving equations (linear, quadratic, absolute value, exponential, logarithm) and inqualities (polynomial, rational, absolute value), functions (definition, notation, evaluation, … endobj Chap ter 2 deals with vector spaces, subspaces, bases, and dimension. << /S /GoTo /D (part.2) >> 51 0 obj