Linear Algebra I
eBook - PDF

Linear Algebra I

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Linear Algebra I

About this book

This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise.This first volume re-examines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book.

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Yes, you can access Linear Algebra I by Frederick P. Greenleaf,Sophie Marques in PDF and/or ePUB format, as well as other popular books in Mathematics & Linear Algebra. We have over one million books available in our catalogue for you to explore.
180
5.
THE
DIAGONALIZATION
PROBLEM
(b)
Prove
that
the
spectral
radius
is
also
given
by
ξ€Έ()
=
lim
ξ€«β†’βˆž
‖

β€–
1/
∞
,
and
explain
why
this
limit
exists.
(c)
Use
equivalence
of
norms
on
matrix
space
M(,
β„‚)
to
show
that
any
other
norm
β€–
βˆ—
β€–
on
matrix
space
yields
the
same
numerical
value
ξ€Έ()
=
lim
ξ€«β†’βˆž
‖

β€–
1/
Hint:
All
vec
tor
space
norms
on
matrix
space
(or
the
space
of
linear
operators
on

)
are
equivalent;
see
Theorem
5.30
and
Ex-
ercise
5.31.
Operator
norms
‖‖
op
were
discussed
in
Example
5.28.

Table of contents

  1. Cover
  2. Title page
  3. Contents
  4. Preface
  5. Chapter 1. Vector Spaces over a Field KK
  6. Chapter 2. Linear Operators 𝐓:𝐕→𝐖
  7. Chapter 3. Duality and the Dual Space symbfit {𝑉*}
  8. Chapter 4. Determinants
  9. Chapter 5. The Diagonalization Problem
  10. Chapter 6. Inner Product Spaces
  11. Index
  12. Back Cover