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

Show that G is isomorphic to G x G

  • oblixps
  • · Replies 5 ·
Replies
5

Graduate Group definition for finite groups

  • thoughtgaze
  • · Replies 16 ·
Replies
16

Matrix Exponential: Find Jordan Form & Compute eA

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Can (I-A)^{-1} Be Expressed as a Series When A^4 = 0?

  • delgeezee
  • · Replies 1 ·
Replies
1

Undergrad Is Matching Dimension Enough for Linear Transformation Invertibility?

  • Bipolarity
  • · Replies 3 ·
Replies
3

High School Algebraic Set Query: Can a Take Any Value?

  • Big-Daddy
  • · Replies 3 ·
Replies
3

Graduate Why is the matrix representation of a linear map unique?

  • Bipolarity
  • · Replies 1 ·
Replies
1

Undergrad Finding the inverse of matrices larger than 2x2

  • dwn
  • · Replies 2 ·
Replies
2

Undergrad Proving a transformation is not linear

  • Bipolarity
  • · Replies 5 ·
Replies
5

Undergrad Linear Transformation involving pi/2

  • dwn
  • · Replies 4 ·
Replies
4

Is (x^2+1) a maximal ideal in Z7[x]?

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Graduate Set of polynomials is infinite dimensional

  • Bipolarity
  • · Replies 6 ·
Replies
6

Undergrad How exactly do you compute the span?

  • Bipolarity
  • · Replies 6 ·
Replies
6

Undergrad How Can I Represent Algebraic Numbers for Computation?

  • Darksonn
  • · Replies 1 ·
Replies
1

Hilbert's Basis Theorem - Basic Question about proof

  • Math Amateur
  • · Replies 1 ·
Replies
1

Graduate Help Understanding Quotient Groups? (Dummit and Foote)

  • robertjordan
  • · Replies 7 ·
Replies
7

Jordan-Basis for Matrix: Need Help!

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Proving Integer Coefficients in Polynomial Rings w/ Gauss Lemma

  • Math Amateur
  • · Replies 2 ·
Replies
2

Product of polynomials over non-integral domain is 0

  • anandvineet27
  • · Replies 5 ·
Replies
5

Graduate Dirichlet's Approximation Theorem not working for n=8 and α= pi?

  • ANphysics
  • · Replies 2 ·
Replies
2

Graduate Extracting a matrix from a curl operation

  • KrayzBlu
  • · Replies 7 ·
Replies
7

Area of Triangle ABC: Calculating with Points A,B,C

  • Petrus
  • · Replies 1 ·
Replies
1

Graduate Is Axiom 2 a Special Case of Axiom 1 in Vector Spaces?

  • cosmic dust
  • · Replies 3 ·
Replies
3

Proving L is an Ideal - Part of the Proof of Hilbert's Bass Theorem

  • Math Amateur
  • · Replies 1 ·
Replies
1

Looking for Linear Algebra Practice Problems?

  • matqkks
  • · Replies 2 ·
Replies
2

Graduate Yes/no question about non-commuting Hermitian operators

  • nomadreid
  • · Replies 2 ·
Replies
2

Principal Ideals and Bezout Domains - (a,b)

  • Math Amateur
  • · Replies 1 ·
Replies
1

Graduate Non-division and grassmass algebras

  • friend
  • · Replies 4 ·
Replies
4

How Do You Calculate the Distance Between Two Skew Lines?

  • Petrus
  • · Replies 19 ·
Replies
19

Graduate Addition to a random matrix element

  • ekkilop
  • · Replies 1 ·
Replies
1

Solving Linear Transformation: Find F Given 3 Equations

  • Petrus
  • · Replies 1 ·
Replies
1

How Does Proposition 7 Support Proposition 15 in Dummit and Foote?

  • Math Amateur
  • · Replies 1 ·
Replies
1

Graduate Leibniz rule and Newton's bionomial theorem

  • ShayanJ
  • · Replies 3 ·
Replies
3

Ask for constructing function from coordinate(x,y) points

  • bundit
  • · Replies 3 ·
Replies
3

Transition Matrix: Polynomial to Coordinate Form

  • Kaspelek
  • · Replies 5 ·
Replies
5

Linear Transform Synonyms: Grouping Components and Spaces

  • Kaspelek
  • · Replies 2 ·
Replies
2

Graduate Is the Wedge Product of Vectors Equal to the Cross Product?

  • Mandelbroth
  • · Replies 15 ·
Replies
15

Graduate How Do You Derive a Vector Function for Taylor Series Expansion?

  • alnoy
  • · Replies 2 ·
Replies
2

Eigenspace (E's question at Yahoo Answers)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Graduate Determine new travel direction

  • levydee
  • · Replies 6 ·
Replies
6

Graduate Representation equivalent to a unitary one

  • Yoran91
  • · Replies 2 ·
Replies
2

Graduate Can a Singular Matrix Have a Unique Solution for Ax=b?

  • Bipolarity
  • · Replies 2 ·
Replies
2

Can Two Lines Intersect? A Proof

  • Petrus
  • · Replies 10 ·
Replies
10

Graduate The vector space of linear transformations

  • Bipolarity
  • · Replies 4 ·
Replies
4
Replies
9

Solving Linear Systems with "m Equations & n Unknowns

  • delgeezee
  • · Replies 4 ·
Replies
4

Undergrad Linear Algebra vs Algebra: Which Is Better for Theoretical Physics?

  • zalba
  • · Replies 8 ·
Replies
8

Graduate When Will the New Twin Prime Paper Be Accessible?

  • PAllen
  • · Replies 1 ·
Replies
1

Graduate Indeterminate limit of the form 1/0

  • Zaurus21
  • · Replies 1 ·
Replies
1

Symbolic calculation in two variables.

  • caffeinemachine
  • · Replies 1 ·
Replies
1

Polynomial Rings - Irreducibility - Proof of Eisenstein's Criteria

  • Math Amateur
  • · Replies 3 ·
Replies
3

Graduate Torsion and Curvature: Understaind The Theory of Curves

  • Tenshou
  • · Replies 5 ·
Replies
5

Ferrari's solution to the quartic

  • mathmaniac1
  • · Replies 1 ·
Replies
1

Specific example of Eisenstein's Theorem using R = Z

  • Math Amateur
  • · Replies 2 ·
Replies
2

Factor Rings of Polynomials Over a Field

  • Math Amateur
  • · Replies 1 ·
Replies
1

Graduate Uniqueness of identity elements for rectangular matrices

  • Bipolarity
  • · Replies 1 ·
Replies
1

Adj ( adj A ) = ( det A )^(n-2) A (ARSLAN's question at Yahoo Answers)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Graduate Which Matrix Norms Are Invariant Under Change of Basis?

  • Heimdall
  • · Replies 1 ·
Replies
1

Undergrad How can I diagonalize this symmetric matrix?

  • Denisse
  • · Replies 1 ·
Replies
1

Determing whether an equation is linear

  • delgeezee
  • · Replies 1 ·
Replies
1

Undergrad Basis of Vectors: Definition & Examples

  • SherlockOhms
  • · Replies 6 ·
Replies
6

High School Why Does the Cross Product of î and ĵ Equal k̂?

  • AakashPandita
  • · Replies 8 ·
Replies
8

Undergrad Reduction of Boolean Expression to its Lowest From

  • George SA
  • · Replies 5 ·
Replies
5

Undergrad Why is the vector equation of a plane defined as n • (r-r0) = 0?

  • That Neuron
  • · Replies 4 ·
Replies
4

Undergrad Linear Algebraic System Solution for Known and constrained variables

  • Ronankeating
  • · Replies 4 ·
Replies
4

Graduate Is this a linear system of equations?

  • nde
  • · Replies 3 ·
Replies
3

Graduate Tensor product of Hilbert spaces

  • Yoran91
  • · Replies 6 ·
Replies
6

Question on the Irreducibility of Polynomials

  • Math Amateur
  • · Replies 1 ·
Replies
1

Cayley table (Asnate's 's question at Yahoo Answers)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Unique Factorization Domain? Nature of Q_Z[x] - 2

  • Math Amateur
  • · Replies 1 ·
Replies
1

How Does Group Theory Apply to Solving a Rubik's Cube?

  • jza
  • · Replies 1 ·
Replies
1

Proving Subspace Properties for Sets of Polynomials in P3

  • chukkitty
  • · Replies 6 ·
Replies
6

Self-adjoint operator (Bens question at Yahoo Answers)

  • Fernando Revilla
  • · Replies 3 ·
Replies
3

Undergrad What are Kyle Numbers and how do you compute them?

  • mahrap
  • · Replies 3 ·
Replies
3

Undergrad What is an Example of a Matrix with Geometric Multiplicity Greater Than 1?

  • njl86
  • · Replies 4 ·
Replies
4

Undergrad The Algebra for Theory of Natural Output

  • JoshMaths
  • · Replies 7 ·
Replies
7

Polynomial Rings and UFDs - Dummit and Foote pages 303-304

  • Math Amateur
  • · Replies 1 ·
Replies
1

Null and non null eigenvalues (Oinker's question at Yahoo Answers)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Trouble with two Galois theory questions

  • LARaiders20
  • · Replies 2 ·
Replies
2

Music Freak's question at Yahoo Answers (Trace in the lnear group)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Matrix of Linear Transformation T with P2: Find, Ker, Im & Inverse

  • Kaspelek
  • · Replies 4 ·
Replies
4

High School Formula for sum of digits of a number

  • greg9381
  • · Replies 5 ·
Replies
5

Graduate Solve Invertible Skew Symmetric Matrix: Hints & Tips

  • Gavroy
  • · Replies 1 ·
Replies
1

Undergrad Finding a transformation between two matrices

  • epsi00
  • · Replies 4 ·
Replies
4

Ali's question at Yahoo Answers (ker f)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Admiral Ackbar's question at Yahoo Answers (Inverse image of a vector)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Order of product of elements in a group

  • Arnold1
  • · Replies 4 ·
Replies
4

Graduate Adjoint operators and diffeomorphism

  • mnb96
  • · Replies 4 ·
Replies
4

Undergrad Linear Transformation using Two Basis

  • Offlinedoctor
  • · Replies 5 ·
Replies
5

Undergrad Find the smallest Matrix for this Kernel

  • germanguy
  • · Replies 1 ·
Replies
1

Undergrad Is Vector Calculus useful for pure math?

  • jameseg
  • · Replies 5 ·
Replies
5

Chris 's question at Yahoo Answers (Inverse of cA)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Undergrad Understanding Subset Requirements in R2 and R3

  • elisemc
  • · Replies 3 ·
Replies
3

Undergrad 3x3 Diagonalizable Matrices over GF(2)

  • ArcanaNoir
  • · Replies 31 ·
2
Replies
31

Undergrad Graphing Parabolas that are not parallel to the y-axis

  • EuroNerd77
  • · Replies 4 ·
Replies
4

Undergrad Geometric Multiplicity of Eigenvalues

  • danielpanatha
  • · Replies 1 ·
Replies
1

PolkaDots 54's question at Yahoo Answers (Diagonalization, conic section))

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Graduate Solve Q(√7,√5) and Prove φ(4√3) = ± 4√3 | Galois Theory Help

  • LARaiders20
  • · Replies 1 ·
Replies
1

Undergrad Are Cube Matrices the Next Frontier in Linear Algebra?

  • Vorde
  • · Replies 3 ·
Replies
3

Graduate Symmetries of a Tetrahedron video

  • MrBeezer
  • · Replies 1 ·
Replies
1