• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
MA135 Vectors and Matrices Samir Siksek
MA135 Vectors and Matrices Samir Siksek

... to argue along the following lines. Let, say, α = 1 + 2i and β = 3 + 4i. Then we check that αβ = −5 + 10i = βα. “So the multiplication of complex numbers is commutative”. Is this an acceptable proof? No, it is not. This is merely an example. It shows that multiplication is commutative for this parti ...
Laplacian Matrices of Graphs: - Computer Science
Laplacian Matrices of Graphs: - Computer Science

1 Definitions - University of Hawaii Mathematics
1 Definitions - University of Hawaii Mathematics

INTRODUCTORY LINEAR ALGEBRA
INTRODUCTORY LINEAR ALGEBRA

Title and Abstracts - Chi-Kwong Li
Title and Abstracts - Chi-Kwong Li

PDF
PDF

CLASS NOTES ON LINEAR ALGEBRA 1. Matrices Suppose that F is
CLASS NOTES ON LINEAR ALGEBRA 1. Matrices Suppose that F is

lecture notes 5
lecture notes 5

... it remains fixed under conjugation by a set of generators of G. Example 1.7. Let’s compute all the subgroups of the symmetric group Σ3 , and let’s see which ones are conjugate to which other ones, and which ones are normal. Using the presentation hσ, τ | σ2 = id, τ3 = id, στ = τ2 σi for Σ3 , we look ...
Triangularizability of Polynomially Compact Operators
Triangularizability of Polynomially Compact Operators

... An operator T on an infinite-dimensional complex Banach space X is called polynomially compact if there exists a non-zero complex polynomial p such that the operator p(T ) is compact. If T k is compact for some k we say that T is a power compact operator. Trivial examples of polynomially compact ope ...
3. Linear function
3. Linear function

Ordinary Differential Equations: A Linear Algebra
Ordinary Differential Equations: A Linear Algebra

GROUP ALGEBRAS. We will associate a certain algebra to a
GROUP ALGEBRAS. We will associate a certain algebra to a

... Proposition 0.3. Let φ : V −→ W be a F [G]-homomorphism. Then ker(φ) and im(φ) are F [G]-submodules of V and W respectively. Definition 0.3. Let G be a finite group, F a field and V a finite dimensional vector space over F . A representation ρ of G on V is a group homomorphism ρ : G −→ GL(V ) A repr ...
HW 2
HW 2

Adaptive Matrix Vector Product
Adaptive Matrix Vector Product

Introduction to the Theory of Linear Operators
Introduction to the Theory of Linear Operators

Discrete Mathematics
Discrete Mathematics

Linear Algebra
Linear Algebra

Parallel numerical linear algebra
Parallel numerical linear algebra

... These issues are locality and regularity of computation. Locality refers to the proximity of the arithmetic and storage components of computers. Computers store data in memories, which are physically separated from the computational units that perform useful arithmetic or logical functions. The time ...
Linear Algebra - Welcome to the University of Delaware
Linear Algebra - Welcome to the University of Delaware

Lie Theory, Universal Enveloping Algebras, and the Poincar้
Lie Theory, Universal Enveloping Algebras, and the Poincar้

Tensors and hypermatrices
Tensors and hypermatrices

... multilinear functional. The next sections discuss the various generalizations of well-known linear algebraic and matrix theoretic notions, such as rank, norm, and determinant, to tensors and hypermatrices. The realization that these notions may be defined for order-d hypermatrices where d > 2 and th ...
OPERATORS OBEYING a-WEYL`S THEOREM Dragan S
OPERATORS OBEYING a-WEYL`S THEOREM Dragan S

Linear Algebra and Differential Equations
Linear Algebra and Differential Equations

... The present text consists of 130 pages of lecture notes, including numerous pictures and exercises, for a one-semester course in Linear Algebra and Differential Equations. The notes are reasonably self-contained. In particular, prior knowledge of Multivariable Calculus is not required. Calculators a ...
arXiv:math/0607084v3 [math.NT] 26 Sep 2008
arXiv:math/0607084v3 [math.NT] 26 Sep 2008

THE ASYMPTOTIC DENSITY OF FINITE
THE ASYMPTOTIC DENSITY OF FINITE

< 1 ... 6 7 8 9 10 11 12 13 14 ... 98 >

Jordan normal form



In linear algebra, a Jordan normal form (often called Jordan canonical form)of a linear operator on a finite-dimensional vector space is an upper triangular matrix of a particular form called a Jordan matrix, representing the operator with respect to some basis. Such matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with identical diagonal entries to the left and below them. If the vector space is over a field K, then a basis with respect to which the matrix has the required form exists if and only if all eigenvalues of the matrix lie in K, or equivalently if the characteristic polynomial of the operator splits into linear factors over K. This condition is always satisfied if K is the field of complex numbers. The diagonal entries of the normal form are the eigenvalues of the operator, with the number of times each one occurs being given by its algebraic multiplicity.If the operator is originally given by a square matrix M, then its Jordan normal form is also called the Jordan normal form of M. Any square matrix has a Jordan normal form if the field of coefficients is extended to one containing all the eigenvalues of the matrix. In spite of its name, the normal form for a given M is not entirely unique, as it is a block diagonal matrix formed of Jordan blocks, the order of which is not fixed; it is conventional to group blocks for the same eigenvalue together, but no ordering is imposed among the eigenvalues, nor among the blocks for a given eigenvalue, although the latter could for instance be ordered by weakly decreasing size.The Jordan–Chevalley decomposition is particularly simple with respect to a basis for which the operator takes its Jordan normal form. The diagonal form for diagonalizable matrices, for instance normal matrices, is a special case of the Jordan normal form.The Jordan normal form is named after Camille Jordan.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report