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 What does Z_2^5 mean in linear algebra notation?

  • TysonM8
  • · Replies 1 ·
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1

Graduate Consequence of the First isomorphism theorem

  • gentsagree
  • · Replies 7 ·
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7

Graduate Does Cayley's Theorem imply all groups are countable?

  • epr1990
  • · Replies 8 ·
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8

Graduate Commutator of exponential operators

  • gentsagree
  • · Replies 7 ·
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7

Undergrad What is the Relationship Between Position and Velocity Vectors?

  • Jhenrique
  • · Replies 6 ·
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6

Graduate Coordinate-free definition of vector spaces

  • "Don't panic!"
  • · Replies 25 ·
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25

Graduate Is Levy-Desplanques Theorem limited to specific values of i and M?

  • Calabi_Yau
  • · Replies 4 ·
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4

Undergrad Solving Linear Systems (Basic Question)

  • Atran
  • · Replies 2 ·
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2

Undergrad What is a vector valued in a function?

  • Jhenrique
  • · Replies 2 ·
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2

Graduate How to Calculate π^σ If We Have 2 Disjoint Cycles?

  • FoxMCloud
  • · Replies 5 ·
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5

Graduate Finding centers of two equal-radius tangent arcs in 3D

  • Brad_
  • · Replies 3 ·
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3

At Least p+1 p-Subgroups in Finite Group G

  • johng1
  • · Replies 2 ·
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2

Undergrad How to find unique solution of X

  • sudipta4
  • · Replies 7 ·
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7

Graduate Misunderstanding a Theorem on Field Homomorphism

  • Mandelbroth
  • · Replies 10 ·
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10

Graduate Factoring algorithms with exponential time complexity

  • paradigmjump
  • · Replies 3 ·
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3

Graduate Why are certain transformations in the case of D4 group considered even or odd?

  • LagrangeEuler
  • · Replies 4 ·
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4

Undergrad Linear system in polar coordinates

  • Jhenrique
  • · Replies 3 ·
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3

Graduate Factor (Quotient) Space definitions.

  • wotanub
  • · Replies 1 ·
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1

Graduate Solutions of a system of linear equations

  • h6ss
  • · Replies 4 ·
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4

Undergrad Quick definition question: Dihedral group

  • srfriggen
  • · Replies 3 ·
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3

Undergrad Can the inverse of a matrix exponential be proven using its definition?

  • GregoryGr
  • · Replies 4 ·
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4

Graduate Why Is a Group with Identical Elements Considered Unfaithful?

  • LagrangeEuler
  • · Replies 1 ·
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1

Sums of Ideals - R. Y. Sharp "Steps in Commutative Algebra"

  • Math Amateur
  • · Replies 2 ·
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2

Is the union of two monoids under a distributive operation a monoid?

  • eddybob123
  • · Replies 14 ·
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14

Graduate An extension of Dot and Cross Product

  • Jhenrique
  • · Replies 10 ·
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10

Describing the ideal (x₁, x₂, ..., xₙ)ᵐ in a polynomial ring

  • Math Amateur
  • · Replies 6 ·
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6

Graduate What Are the Utilities of Interior and Exterior Products?

  • Jhenrique
  • · Replies 1 ·
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1

Ring adjunction: showing S[Γ∪Δ]=S[Γ][Δ]

  • Math Amateur
  • · Replies 16 ·
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16

Graduate Proving Rank(G/H) = Rank(G) - Rank(H) for free abelian groups

  • nonequilibrium
  • · Replies 2 ·
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2

Graduate What Symmetry Group Does the Quantum Harmonic Oscillator Exhibit?

  • LagrangeEuler
  • · Replies 5 ·
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5

Undergrad Eigenvalues of 2 matrices are equal

  • gopi9
  • · Replies 1 ·
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1
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4

Products of ideals of K[x1, x2, x3, x4]

  • Math Amateur
  • · Replies 8 ·
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8

Residue Class Rings (Factor Rings) of Polynomials _ R Y Sharp

  • Math Amateur
  • · Replies 4 ·
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4

How to solve exercises with 2D and 3D vectors and dot product

  • Kalbaan
  • · Replies 3 ·
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3

Graduate Face of face of a cone is a face. Proof?

  • Silversonic
  • · Replies 4 ·
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4

Graduate Is the Levi-Civita tensor symmetric to any group?

  • nateHI
  • · Replies 2 ·
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2

Graduate Group Theory, unitary representation and positive eigenvalues

  • Aradan
  • · Replies 3 ·
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3

Graduate Injective endomorphism = Surjective endomorphism

  • Daaavde
  • · Replies 6 ·
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6

Undergrad Ray tracing, regarding Turner Whitted's original paper

  • alan_k
  • · Replies 2 ·
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2

Undergrad Algebra with Complex Numbers & Imaginary Unit

  • aaaa202
  • · Replies 44 ·
2
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44

Polynomial Rings - Lemma 1.13 from Sharp: Steps in Commutative Algebra

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Kernels and determinants of a matrix

  • gentsagree
  • · Replies 5 ·
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5

Undergrad What is the minimum rank of a skew symmetric matrix?

  • bhanesh
  • · Replies 5 ·
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5

Graduate Is Dimension 3 Enough to Prove Isomorphism Between Spaces?

  • Daaavde
  • · Replies 6 ·
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6

Graduate Diagonalizable endomorphism has trivial null space

  • Daaavde
  • · Replies 6 ·
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6

Using matrix to complete the square

  • PhizKid1
  • · Replies 4 ·
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4

Quasi-local commutative ring with maximal ideal M

  • Math Amateur
  • · Replies 16 ·
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16

Graduate F=ℝ: Normal matrix with real eigenvalues but not diagonalizable

  • Bipolarity
  • · Replies 1 ·
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1

Find all maximal ideals of K[X] where K is a field

  • Math Amateur
  • · Replies 8 ·
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8
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5

Zero-Trace Symmetric Matrix is Orthogonally Similar to A Zero-Diagonal Matrix.

  • caffeinemachine
  • · Replies 5 ·
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5

Graduate What is the New Definition of Conformal Transformations?

  • gentsagree
  • · Replies 1 ·
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1

Graduate Number of jordan blocks in Jordan decomposition

  • jinawee
  • · Replies 3 ·
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3

Undergrad Order of permutations in symmetric group Sn

  • ZZ Specs
  • · Replies 10 ·
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10

Undergrad How to visualise bilinear form and inner products?

  • mathmo94
  • · Replies 3 ·
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3

Graduate Why is the morphism to C an epimorphism in a short exact sequence?

  • gentsagree
  • · Replies 2 ·
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2

Graduate Cosets: difference between these two statements

  • ZZ Specs
  • · Replies 2 ·
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2

Graduate Do Orthogonal Subsets Spanning the Same Subspace Prove Equality?

  • NATURE.M
  • · Replies 4 ·
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4

Graduate SVD Low-Rank Approximation Algorithm

  • TheOldHag
  • · Replies 8 ·
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8

Prime ideals of K[X] where K is a field

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Why delete the origin from R³ to define the projective plane

  • gentsagree
  • · Replies 6 ·
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6

Proving End($K^2$)=K for A-Module $K^2$

  • Fermat1
  • · Replies 7 ·
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7

Graduate How Can I Publish My Beal Conjecture Findings?

  • alberto4188
  • · Replies 1 ·
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1

Linear Dependency: Max Size of Subset of Vectors

  • Yankel
  • · Replies 2 ·
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2

Graduate Is it possible to express all mathematics through atomic pieces of computation?

  • tanus5
  • · Replies 3 ·
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3

Compute Ideal Generated by Matrix 3x3

  • Fermat1
  • · Replies 5 ·
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5

Is \( A \) Isomorphic to \( \dfrac{R<X,Y>}{((X^2+1)X,(X^2+1)Y,YX)} \)?

  • Fermat1
  • · Replies 3 ·
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3

Graduate Is the Laplace transform a group homomorphism or isomorphism?

  • LagrangeEuler
  • · Replies 7 ·
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7

Algebra: Generating C as an R Algebra Subject to i^2=-1

  • Fermat1
  • · Replies 5 ·
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5

Why is Sharp's Lemma 1.10 crucial for understanding R-algebras?

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Linear algebra, when does the implications hold?

  • bobby2k
  • · Replies 3 ·
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3

Maximal ideals of K[X] where K is a field

  • Math Amateur
  • · Replies 8 ·
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8

Undergrad Multiple Choise Questions in Calculus/Algebra/Electromagnetism

  • Magna Visus
  • · Replies 2 ·
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2

Number of elements and subgroups

  • kalish1
  • · Replies 1 ·
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1

Graduate Why does the SVD low rank approximation still have full rank?

  • TheOldHag
  • · Replies 5 ·
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5

Undergrad Are Matrix Multiplication Rules the Same for Composing Linear Transformations?

  • 1MileCrash
  • · Replies 3 ·
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3

Matrix transform- about origin, then angular rotation

  • Jundoe
  • · Replies 4 ·
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4

Graduate Are orthonormal eigenbases unique?

  • Bipolarity
  • · Replies 5 ·
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5

What is the fastest method for computing determinants?

  • Jundoe
  • · Replies 10 ·
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10

Graduate Set of invertible matrices with real entries

  • LagrangeEuler
  • · Replies 3 ·
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3

Prove These 3 Statements About A Matrix: Rank of Adjoint

  • Yankel
  • · Replies 1 ·
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1

Graduate Is $\mathcal{R}$ Lie Group Without 0?

  • LagrangeEuler
  • · Replies 11 ·
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11

Is the Orthogonal Complement of an Invariant Subspace Itself Invariant?

  • Sudharaka
  • · Replies 2 ·
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2

Undergrad Orthogonal Projections vs Non-orthogonal projections?

  • rayzhu52
  • · Replies 1 ·
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1

Prove that every nonzero vector in V is a maximal vector for T.

  • toni07
  • · Replies 4 ·
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4

Graduate Product of two Minkowksi metrics

  • gentsagree
  • · Replies 1 ·
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1

Distance Between a Subspace and a Vector

  • Sudharaka
  • · Replies 2 ·
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2

Undergrad Determinant of a unit columns matrix

  • hedipaldi
  • · Replies 7 ·
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7

Graduate Left inverse of rectangular matrices when only right inverse exists

  • genxium
  • · Replies 10 ·
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10

Distance from a vector to a subspace

  • smile1
  • · Replies 6 ·
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6

High School Are orientation and direction the same thing for vectors?

  • chemistry1
  • · Replies 3 ·
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3

Ideal structure for V = {(0,0), (1,1)} over F_2 in A^2

  • Math Amateur
  • · Replies 9 ·
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9

What is the annihilator of a tensor in vector space V?

  • Sudharaka
  • · Replies 1 ·
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1

Jordan Normal Form of Unitary Transformation

  • Sudharaka
  • · Replies 2 ·
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2
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2

Finding Basis of the Quotient Space

  • Sudharaka
  • · Replies 9 ·
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9

Semigroup Structure: Exploiting Non-Finitely Generated Monoids

  • mathbalarka
  • · Replies 7 ·
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7

Solving Systems of Linear Equations with ljx.m

  • mathmari
  • · Replies 1 ·
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1

Undergrad Is the Matrix R Necessarily Lower Triangular in Matrix Decomposition?

  • Jano L.
  • · Replies 3 ·
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3