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

Undergrad Solving a system of equation with matrices

  • Mr Davis 97
  • · Replies 4 ·
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4

Undergrad Simple Modules and Maximal Right Ideals ....

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Jacobson Radical and Right Annihilator Ideals ....

  • Math Amateur
  • · Replies 1 ·
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1
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1

Undergrad Prove that V is the internal direct sum of two subspaces

  • Austin Chang
  • · Replies 7 ·
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7

Undergrad How can I find the orthogonal matrix that diagonalises a given matrix?

  • spaghetti3451
  • · Replies 22 ·
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22

Undergrad What is the concept of tensor product and how is it used in mathematics?

  • fog37
  • · Replies 5 ·
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5

Undergrad Understanding Vector Spaces with functions

  • Austin Chang
  • · Replies 24 ·
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24

Which is the linear system of equations?

  • mathmari
  • · Replies 10 ·
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10

Graduate Isomorphism concepts,( example periods elliptic functions )

  • binbagsss
  • · Replies 8 ·
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8

Graduate Can Hermitian Matrices be Traceless?

  • SgrA*
  • · Replies 7 ·
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7

Proof of Bland's Example 13: Simple Modules and Quotients of Maximal Modules

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Simple Modules and quotients of maximal modules, Bland Ex 13

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Kronecker product recovering the initial representation?

  • arivero
  • · Replies 1 ·
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1

Undergrad DIfference between vectors and relations of points

  • Mr Davis 97
  • · Replies 10 ·
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10

Undergrad Matrices and linear transformations. Where did I go wrong?

  • davidge
  • · Replies 2 ·
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2

Undergrad Vector Space: Scalar Restriction in ℤ2

  • Austin Chang
  • · Replies 2 ·
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2

Calculating Determinants of Matrices: A How-To Guide

  • mathmari
  • · Replies 5 ·
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5

High School Group of Symmetry of Rectangle: Reflections & Diagonals

  • LagrangeEuler
  • · Replies 8 ·
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8

Undergrad Existence of spanning set for every vector space

  • Mr Davis 97
  • · Replies 5 ·
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5

Undergrad Commutative diagrams and equality of composition

  • Mr Davis 97
  • · Replies 1 ·
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1
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10

Is the transformation matrix of $\Phi$ in relation to $B$ correct?

  • mathmari
  • · Replies 7 ·
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7

Graduate Is Group Operation in (G,*) Considered Composition in Mathematics?

  • LagrangeEuler
  • · Replies 5 ·
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5

Undergrad Is a symmetric matrix with positive eigenvalues always real?

  • TeethWhitener
  • · Replies 8 ·
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8

Undergrad Some questions about linear transformation

  • Eus
  • · Replies 1 ·
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1

Undergrad Terminology for Substructures in Vector Spaces

  • Mr Davis 97
  • · Replies 2 ·
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2

Undergrad Are Splitting Fields Unique for Different Polynomial Families?

  • PsychonautQQ
  • · Replies 1 ·
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1

Undergrad Jacobson Radical and Direct Sums - Bland, Proposition 6.1.4

  • Math Amateur
  • · Replies 3 ·
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3

Jacobson Radical and Direct Sums - Bland, Proposition 6.1.4 ....

  • Math Amateur
  • · Replies 4 ·
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4

Does \(B\) Span Algebraically \(E\) Over \(F\)?

  • mathmari
  • · Replies 1 ·
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1

Exponent of Group Hey! :o - Answers to Questions

  • mathmari
  • · Replies 16 ·
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16

Undergrad Is the trace of a matrix independent of basis?

  • Trixie Mattel
  • · Replies 3 ·
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3

It is an algebraically dependent set over F

  • mathmari
  • · Replies 4 ·
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4

Undergrad Understanding Separable Vector Spaces: The Basics Explained

  • fog37
  • · Replies 9 ·
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9

Field extensions and Galois goup

  • mathmari
  • · Replies 2 ·
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2

Diagonalizable Matrix: How to Approach?

  • Yankel
  • · Replies 4 ·
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4

Undergrad Definition of discrete Subgroup quick q

  • binbagsss
  • · Replies 10 ·
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10

Is $\Phi|_{U_2}$ a Vector Space Isomorphism?

  • mathmari
  • · Replies 1 ·
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1

Injective linear mapping - image

  • mathmari
  • · Replies 2 ·
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2

Undergrad Proving an inverse of a groupoid is unique

  • Matejxx1
  • · Replies 4 ·
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4

Graduate Real parameters and imaginary generators

  • Heisenberg1993
  • · Replies 3 ·
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3

Undergrad Using determinant to find constraints on equation

  • TheDemx27
  • · Replies 4 ·
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4

Undergrad Basis of a Subspace of a Vector Space

  • fog37
  • · Replies 8 ·
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8

Undergrad Linear algebra ( symmetric matrix)

  • Vijay Raghavan
  • · Replies 2 ·
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2

Graduate Question regarding root of Bring quintic not expressible with radicals

  • Buzz Bloom
  • · Replies 37 ·
2
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37

Solving Linear Mapping Problems with Matrix $M$ in $\mathbb K^2$

  • mathmari
  • · Replies 10 ·
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10

Pointwise and uniform convergence

  • mathmari
  • · Replies 5 ·
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5

Solving for Invertible Matrix: What Am I Doing Wrong?

  • Yankel
  • · Replies 3 ·
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3
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1

What is the Intuition Behind Integral Over in Commutative Algebra?

  • A.Magnus
  • · Replies 2 ·
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2
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8

Undergrad Jacobson Radical and Rad(M) - Bland Corollary 6.1.3 ....

  • Math Amateur
  • · Replies 10 ·
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10

How Can We Prove the Inequality of Rank Matrices?

  • mathmari
  • · Replies 8 ·
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8

Graduate How do I supply arpack drivers with all starting vectors?

  • Jimmy and Bimmy
  • · Replies 1 ·
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1

Graduate Justify matrices form basis for SO(4)

  • OhNoYaDidn't
  • · Replies 5 ·
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5

Undergrad Eistenstein series E_k(t=0) quick q? Modular forms

  • binbagsss
  • · Replies 1 ·
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1

Jacobson Radical and Rad(M) - Bland Corollary 6.1.3 ....

  • Math Amateur
  • · Replies 7 ·
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7

Determining a determinant using recurrence relations

  • karseme
  • · Replies 1 ·
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1

Undergrad Congruence Subgroups and Modular Forms Concept Questions

  • binbagsss
  • · Replies 1 ·
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1

How can we prove that E/Q is a normal extension?

  • mathmari
  • · Replies 1 ·
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1

Finitely Generated Modules and Maximal Submodules

  • Math Amateur
  • · Replies 2 ·
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2

Why is this polynomial separable?

  • mathmari
  • · Replies 10 ·
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10

Graduate Representation number via quad forms of theta quadratic form

  • binbagsss
  • · Replies 6 ·
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6

Graduate Applying group theory to multivariate eqs

  • Stephen Tashi
  • · Replies 4 ·
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4

Showing that P_3 is a subspace to P_n

  • cbarker1
  • · Replies 6 ·
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6

Eisenstein polynomial and field extension

  • mathmari
  • · Replies 24 ·
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24

Is t Algebraic Over F(S) in Field Extension E/F?

  • mathmari
  • · Replies 5 ·
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5

Defining & Proving Modulo Multiplication in $\mathbb{Z}_k$

  • mathmari
  • · Replies 3 ·
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3

Undergrad Can we retrieve the inverse of matrix A in this example?

  • Adel Makram
  • · Replies 14 ·
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14

Graduate Matrix Lie groups and its Lie Algebra

  • Xico Sim
  • · Replies 7 ·
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7

Undergrad Modular form quick question translation algebra

  • binbagsss
  • · Replies 1 ·
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1

Undergrad Multiplying a vector by a complex number

  • topito2
  • · Replies 8 ·
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8

Undergrad Geometric Algebra formulation of Quantum Mechanics

  • Milsomonk
  • · Replies 6 ·
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6

Why does this hold when we have the zero matrix?

  • mathmari
  • · Replies 7 ·
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7

Undergrad Show that you can find d and b s.t pd-bq=1 , p and q are coprime- GCF

  • binbagsss
  • · Replies 4 ·
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4

Can You Successfully Factorize x^2+y^2+z^2-2xy-2yz-2zx?

  • anemone
  • · Replies 2 ·
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2

High School Factoring trick by determining a zero value

  • CynicusRex
  • · Replies 2 ·
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2

Undergrad Automorphisms of Central Simple Algebras/Bresar Example 1.27

  • Math Amateur
  • · Replies 2 ·
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2

Determining Basis and Dimension for Vector Subspaces $U_1$ and $U_2$

  • mathmari
  • · Replies 5 ·
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5

Insights Representations and Why Precision is Important

  • fresh_42
  • · Replies 2 ·
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2

How to Extend These Vectors to a Basis in $\mathbb{R}^4$?

  • mathmari
  • · Replies 4 ·
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4

Determine the vectors of components

  • mathmari
  • · Replies 1 ·
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1

Graduate Using Cayley-Hamilton Theorem to Calculate Matrix Powers

  • AcidRainLiTE
  • · Replies 1 ·
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1

Solve Vector Space Question: Get the Solution Now

  • LearnerJr
  • · Replies 3 ·
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3

How to Quickly Find the Rank of a 4 x 6 Matrix Using Column Operations

  • A.Magnus
  • · Replies 2 ·
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2

Find the General Expression for a Linear Transformation

  • Leanna
  • · Replies 4 ·
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4

Undergrad Multiplication Maps on Algebras .... Bresar, Lemma 1.25 ....

  • Math Amateur
  • · Replies 11 ·
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11

Undergrad Calculating the Area of an Apollonian Gasket: A Formula for n Layers

  • caters
  • · Replies 7 ·
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7

Automorphisms of Central Simple Algebras - Bresar Example 1.27 .... ....

  • Math Amateur
  • · Replies 3 ·
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3
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2

No prefix added: How do I find a basis of a $\mathbb{R}$-vector space?

  • mathmari
  • · Replies 14 ·
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14

Undergrad Multiplication Maps on Algebras .... Further questions ....

  • Math Amateur
  • · Replies 2 ·
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2

Are $V_1$ and $V_2$ Vector Spaces According to Defined Properties?

  • mathmari
  • · Replies 14 ·
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14

Undergrad Prove the sequence is exact: 0 → ker(f) → V → im(f) → 0

  • Apothem
  • · Replies 1 ·
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1

Undergrad Left/Right Multiplication Maps on Algebras .... Bresar

  • Math Amateur
  • · Replies 2 ·
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2

Simple Unitial Rings .... centre is a field .... ? ....

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Wedge product of basis vectors

  • Kevin McHugh
  • · Replies 4 ·
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4

Characteristic Equations and Commutativity

  • A.Magnus
  • · Replies 7 ·
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7

Undergrad Simple Unitial Rings .... centre is a field .... ? ....

  • Math Amateur
  • · Replies 2 ·
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2