Linear and Abstract Algebra Forum

Join experts in discussing linear and abstract algebra topics. This includes vector spaces and linear transformations. Also groups and other algebraic structures along with Number Theory.

Threads

High School Linearizing a Relation: How to Create a Best Fit Linear Line in Logger Pro

  • ChanYoung Park
  • · Replies 4 ·
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4

Intersection of all subspace of V is the empty set

  • mathmari
  • · Replies 8 ·
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8

Undergrad Relationship between a non-Hermitian Hamiltonian and its solution

  • SeM
  • · Replies 2 ·
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2

Describe bases for the span of sets

  • mathmari
  • · Replies 8 ·
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8

Graduate Finding Angles of Triangle Given Two Points on Earth and One in Space

  • Boxturtle
  • · Replies 9 ·
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9

Undergrad Consequences on a system of ODEs after performing operations

  • SeM
  • · Replies 4 ·
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4

Undergrad Types of complex matrices, why only 3?

  • SeM
  • · Replies 5 ·
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5

Undergrad A different way to express the span

  • Raymondyhq
  • · Replies 8 ·
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8

Graduate How to prove vector identities WITHOUT using levi civita ?

  • darksilence
  • · Replies 2 ·
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2

Undergrad Is the Frobenius Norm a Reliable Indicator of Matrix Conditioning?

  • SeM
  • · Replies 2 ·
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2

Smallest subfield of C that contains i

  • mathmari
  • · Replies 4 ·
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4

Undergrad How to check if a matrix is Hilbert space and unitary?

  • SeM
  • · Replies 16 ·
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16

High School Why does a matrix diagonalise in this case?

  • Wrichik Basu
  • · Replies 2 ·
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2

Graduate Commutation and Non-Linear Operators

  • MisterX
  • · Replies 5 ·
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5

Undergrad How to study an ODE in matrix form in a Hilbert space?

  • SeM
  • · Replies 6 ·
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6

Eigenvector Calculations and Verification for y1+y2=5

  • ertagon2
  • · Replies 2 ·
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2

Questions about analysis of algorithm

  • evinda
  • · Replies 5 ·
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5

Proving the Equality of A and B: A+B=0 or A=B

  • solakis1
  • · Replies 2 ·
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2

Undergrad Bases, operators and eigenvectors

  • fog37
  • · Replies 7 ·
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7

Undergrad What does this vector notation mean?

  • Yealtas
  • · Replies 3 ·
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3

Undergrad Can a Hermitian matrix have complex eigenvalues?

  • SeM
  • · Replies 4 ·
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4

Undergrad Doubt about proof on self-adjoint operators.

  • Rodrigo Schmidt
  • · Replies 3 ·
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3

Insights What Are Eigenvectors and Eigenvalues? - Comments

  • Mark44
  • · Replies 28 ·
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28

Undergrad What is the equivalent of a group in category theory?

  • Krunchyman
  • · Replies 8 ·
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8

Undergrad How many generators can a cyclic group have by definition?

  • lintmintskint
  • · Replies 7 ·
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7

Undergrad Why can't a set of vectors with less than n elements span ℝn?

  • Drakkith
  • · Replies 21 ·
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21

Undergrad Notation for systems of simultaneous equations

  • Benjamin Irwin
  • · Replies 4 ·
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4

Undergrad How to find the matrix of the derivative endomorphism?

  • Cathr
  • · Replies 2 ·
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2

Graduate On the equivalent definitions for solvable groups

  • hihiip201
  • · Replies 3 ·
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3

How to Find the Zeros Using the Rational Roots Theorem?

  • Elissa89
  • · Replies 8 ·
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8

Undergrad Can a shear operation introduce a new linear dependency?

  • swampwiz
  • · Replies 12 ·
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12

Undergrad Help Needed: Understanding Hungerford's Algebra Book Proofs

  • mr.tea
  • · Replies 4 ·
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4

Undergrad What is the definition of a matrix in function form?

  • Nipon Waiyaworn
  • · Replies 9 ·
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9

How does the row picture differ from the column picture in linear systems?

  • otownsend
  • · Replies 1 ·
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1

Insights What Is a Tensor? The mathematical point of view

  • fresh_42
  • · Replies 57 ·
2
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57

Undergrad Terminology involving "homomorphic"

  • Stephen Tashi
  • · Replies 19 ·
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19

What Is Required to Prove a Subset is a Vector Space?

  • Yankel
  • · Replies 3 ·
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3

Undergrad Groups of Automorphisms - Aut(C) ....

  • Math Amateur
  • · Replies 19 ·
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19

Undergrad Groups of Automporphisms - remarks by Anderson and Feil ....

  • Math Amateur
  • · Replies 23 ·
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23

Undergrad Understanding Quaternion Transformations for 3D Vectors

  • Tio Barnabe
  • · Replies 4 ·
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4

Undergrad How can there only be two possible four-element groups?

  • Azure Ace
  • · Replies 6 ·
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6

Undergrad Are my thoughts about groups correct?

  • Tio Barnabe
  • · Replies 1 ·
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1

Undergrad Why does Gaussian elimination work?

  • Mathematicsss
  • · Replies 5 ·
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5

High School Define Vector on x-Axis: -d/2 to d/2

  • Philosophaie
  • · Replies 1 ·
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1

Undergrad Linear Program:Multiple Optima for multivariable Obj. Func.?

  • StevenJacobs990
  • · Replies 1 ·
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1

Undergrad Question about group representation

  • Tio Barnabe
  • · Replies 3 ·
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3

Calculating Ratio of Determinants for $a,b$ Real Coefficients

  • lfdahl
  • · Replies 2 ·
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2

Undergrad Exterior Algebra: (A1−A2,B1−B2,C1−C2) ∧ (A1,B1,C1) Explained

  • Philosophaie
  • · Replies 1 ·
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1

Undergrad Eigenvalues of Circulant matrices

  • mr.tea
  • · Replies 1 ·
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1

Graduate Finding Eigenvectors with Lanczos Algorithm

  • maverick_starstrider
  • · Replies 1 ·
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1
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5

Understand Proof for Exterior Product Proposition

  • mathmari
  • · Replies 2 ·
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2

Undergrad Is Euclidean Space Inherently Geometric or Just a Vector Space?

  • FallenApple
  • · Replies 32 ·
2
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32

Undergrad Is My Panel Data Sample Size Adequate and Modeling Approach Correct?

  • beaf123
  • · Replies 4 ·
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4

Graduate Infinite Basis and Supernatural Numbers

  • FallenApple
  • · Replies 9 ·
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9

Undergrad Finding the Kernel of a Matrix Map

  • WWGD
  • · Replies 11 ·
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11

Undergrad Solving System of Equations w/ Gauss-Jordan Elimination

  • Oannes
  • · Replies 3 ·
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3

Undergrad Matrix for transforming vector components under rotation

  • saadhusayn
  • · Replies 2 ·
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2

Undergrad Homomorphism of an elementwise sum and dot product

  • NotASmurf
  • · Replies 1 ·
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1

Undergrad How Do Eigenvalues of Block Matrices Relate to Their Sub-Matrices and Graphs?

  • Adel Makram
  • · Replies 11 ·
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11

Undergrad Transforming a Matrix: Elementary Methods for Finite Fields

  • Lapidus
  • · Replies 8 ·
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8

High School Vector Proof: Solving for IuI and IvI using Dot Product Properties

  • stolencookie
  • · Replies 10 ·
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10

Graduate Gershgorin Circle Theorem, mathematical derivation of eigenvalue estimates

  • onako
  • · Replies 2 ·
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2

Graduate Numerically Calculating Eigenvalues

  • member 428835
  • · Replies 12 ·
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12

Undergrad Solving a system of linear equations using back substitution

  • Jen2114
  • · Replies 1 ·
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1

Undergrad Addition of exponents proof in group theory

  • Mr Davis 97
  • · Replies 5 ·
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5

High School Looking for some intuition on a basic Algebra equation

  • DS2C
  • · Replies 8 ·
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8

Undergrad How can -a be equal to (-1)*a?

  • transmini
  • · Replies 6 ·
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6

High School What is the requirement for something to qualify as vector?

  • Wrichik Basu
  • · Replies 6 ·
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6

Undergrad Are there relations that are valid for any field?

  • SVN
  • · Replies 5 ·
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5

Graduate Understanding Rank of a Matrix: Important Theorem and Demonstration

  • Conrad Manfried
  • · Replies 5 ·
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5

Undergrad Inner Product vs. Dot Product Confusion in Quantum Physics?

  • lawlieto
  • · Replies 4 ·
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4

Graduate Transformation of the neighborhood of a branch point

  • Eric_H
  • · Replies 4 ·
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4

High School Generalized Linear equation of a cube

  • Leo Authersh
  • · Replies 5 ·
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5

Undergrad Spectral Bisection of Simplest Graph Clearly Incorrect

  • maverick_starstrider
  • · Replies 5 ·
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5

High School How Do Rotation Matrices Impact Coordinate Systems and Object Transformations?

  • Leo Authersh
  • · Replies 6 ·
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6

Graduate Selected solution of linear equations

  • Gabor Ladanyi
  • · Replies 8 ·
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8

Undergrad Lie Algebra states of a representation

  • Silviu
  • · Replies 5 ·
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5

Hcc8.12 Find the sum of vectors

  • karush
  • · Replies 6 ·
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6

Undergrad Normal modes using representation theory

  • Silviu
  • · Replies 3 ·
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3

Undergrad Finite and infinitesimal Rotations

  • Josh1079
  • · Replies 2 ·
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2

Undergrad Advantages of Vector Spaces over Modules

  • FallenApple
  • · Replies 4 ·
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4

Undergrad Matrix Equation -- clarification about solving a system

  • member 428835
  • · Replies 16 ·
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16

Undergrad Is zero vector always present in any n-dimensional space?

  • Asad Raza
  • · Replies 7 ·
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7

Undergrad How do I know if a matrix is positive definite?

  • Telemachus
  • · Replies 11 ·
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11

Graduate Algebraic structure in time evolution

  • tom.stoer
  • · Replies 5 ·
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5

Undergrad Need help solving for X in third order polynomial

  • Dubs Mozz
  • · Replies 15 ·
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15

Undergrad SU(2) Generators: Understanding Lie Algebra

  • Silviu
  • · Replies 17 ·
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17

Graduate If [A,B]=0, are they both functions of some other operator?

  • pantheid
  • · Replies 5 ·
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5

Undergrad Index (killing form ?) in a reducible representation

  • hideelo
  • · Replies 1 ·
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1

Graduate How to Calculate the Rotation Axis Incorporating Translation?

  • Daniel Thuresson
  • · Replies 8 ·
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8

When does a reflection around a point result in a reflection along a line?

  • mathmari
  • · Replies 20 ·
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20

Graduate How to prove The Cayley-Hamilton Theorem?

  • Nipon Waiyaworn
  • · Replies 18 ·
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18

Undergrad Proving Matrix Exponential Theorem: Unipotent & Nilpotent

  • Josh1079
  • · Replies 1 ·
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1

Graduate Summing simple histograms to recreate a more complex one

  • Master Sidoshi
  • · Replies 2 ·
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2

Undergrad Injectivity equivalent to having a left inverse

  • Mr Davis 97
  • · Replies 1 ·
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1
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5
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24

Conditions so that the determinant is zero

  • mathmari
  • · Replies 14 ·
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14

Mappings - Similarity transformations

  • mathmari
  • · Replies 9 ·
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9