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.
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Undergrad What does Z_2^5 mean in linear algebra notation?
- TysonM8
- · Replies 1 ·
Graduate Consequence of the First isomorphism theorem
- gentsagree
- · Replies 7 ·
Graduate Does Cayley's Theorem imply all groups are countable?
- epr1990
- · Replies 8 ·
Graduate Commutator of exponential operators
- gentsagree
- · Replies 7 ·
Undergrad What is the Relationship Between Position and Velocity Vectors?
- Jhenrique
- · Replies 6 ·
Graduate Coordinate-free definition of vector spaces
- "Don't panic!"
- · Replies 25 ·
Graduate Is Levy-Desplanques Theorem limited to specific values of i and M?
- Calabi_Yau
- · Replies 4 ·
Undergrad Solving Linear Systems (Basic Question)
- Atran
- · Replies 2 ·
Undergrad What is a vector valued in a function?
- Jhenrique
- · Replies 2 ·
Graduate How to Calculate π^σ If We Have 2 Disjoint Cycles?
- FoxMCloud
- · Replies 5 ·
Graduate Finding centers of two equal-radius tangent arcs in 3D
- Brad_
- · Replies 3 ·
At Least p+1 p-Subgroups in Finite Group G
- johng1
- · Replies 2 ·
Undergrad How to find unique solution of X
- sudipta4
- · Replies 7 ·
Graduate Misunderstanding a Theorem on Field Homomorphism
- Mandelbroth
- · Replies 10 ·
Graduate Factoring algorithms with exponential time complexity
- paradigmjump
- · Replies 3 ·
Graduate Why are certain transformations in the case of D4 group considered even or odd?
- LagrangeEuler
- · Replies 4 ·
Undergrad Linear system in polar coordinates
- Jhenrique
- · Replies 3 ·
Graduate Factor (Quotient) Space definitions.
- wotanub
- · Replies 1 ·
Graduate Solutions of a system of linear equations
- h6ss
- · Replies 4 ·
Undergrad Quick definition question: Dihedral group
- srfriggen
- · Replies 3 ·
Undergrad Can the inverse of a matrix exponential be proven using its definition?
- GregoryGr
- · Replies 4 ·
Graduate Why Is a Group with Identical Elements Considered Unfaithful?
- LagrangeEuler
- · Replies 1 ·
Sums of Ideals - R. Y. Sharp "Steps in Commutative Algebra"
- Math Amateur
- · Replies 2 ·
Is the union of two monoids under a distributive operation a monoid?
- eddybob123
- · Replies 14 ·
Graduate An extension of Dot and Cross Product
- Jhenrique
- · Replies 10 ·
Describing the ideal (x₁, x₂, ..., xₙ)ᵐ in a polynomial ring
- Math Amateur
- · Replies 6 ·
Graduate What Are the Utilities of Interior and Exterior Products?
- Jhenrique
- · Replies 1 ·
Ring adjunction: showing S[Γ∪Δ]=S[Γ][Δ]
- Math Amateur
- · Replies 16 ·
Graduate Proving Rank(G/H) = Rank(G) - Rank(H) for free abelian groups
- nonequilibrium
- · Replies 2 ·
Graduate What Symmetry Group Does the Quantum Harmonic Oscillator Exhibit?
- LagrangeEuler
- · Replies 5 ·
Undergrad Eigenvalues of 2 matrices are equal
- gopi9
- · Replies 1 ·
Show Self-Adjointness of Operator E on $L_{2}$ of Square Integrable Functions
- Fermat1
- · Replies 4 ·
Products of ideals of K[x1, x2, x3, x4]
- Math Amateur
- · Replies 8 ·
Residue Class Rings (Factor Rings) of Polynomials _ R Y Sharp
- Math Amateur
- · Replies 4 ·
How to solve exercises with 2D and 3D vectors and dot product
- Kalbaan
- · Replies 3 ·
Graduate Face of face of a cone is a face. Proof?
- Silversonic
- · Replies 4 ·
Graduate Is the Levi-Civita tensor symmetric to any group?
- nateHI
- · Replies 2 ·
Graduate Group Theory, unitary representation and positive eigenvalues
- Aradan
- · Replies 3 ·
Graduate Injective endomorphism = Surjective endomorphism
- Daaavde
- · Replies 6 ·
Undergrad Ray tracing, regarding Turner Whitted's original paper
- alan_k
- · Replies 2 ·
Undergrad Algebra with Complex Numbers & Imaginary Unit
- aaaa202
- · Replies 44 ·
Polynomial Rings - Lemma 1.13 from Sharp: Steps in Commutative Algebra
- Math Amateur
- · Replies 6 ·
Undergrad Kernels and determinants of a matrix
- gentsagree
- · Replies 5 ·
Undergrad What is the minimum rank of a skew symmetric matrix?
- bhanesh
- · Replies 5 ·
Graduate Is Dimension 3 Enough to Prove Isomorphism Between Spaces?
- Daaavde
- · Replies 6 ·
Graduate Diagonalizable endomorphism has trivial null space
- Daaavde
- · Replies 6 ·
Using matrix to complete the square
- PhizKid1
- · Replies 4 ·
Quasi-local commutative ring with maximal ideal M
- Math Amateur
- · Replies 16 ·
Graduate F=ℝ: Normal matrix with real eigenvalues but not diagonalizable
- Bipolarity
- · Replies 1 ·
Find all maximal ideals of K[X] where K is a field
- Math Amateur
- · Replies 8 ·
Solve 3D Vector Equation: x-int=3, z-int=-1; (x,y,z)=(p1,p2,p3)+t(d1,d2,d3)
- Raerin
- · Replies 5 ·
Zero-Trace Symmetric Matrix is Orthogonally Similar to A Zero-Diagonal Matrix.
- caffeinemachine
- · Replies 5 ·
Graduate What is the New Definition of Conformal Transformations?
- gentsagree
- · Replies 1 ·
Graduate Number of jordan blocks in Jordan decomposition
- jinawee
- · Replies 3 ·
Undergrad Order of permutations in symmetric group Sn
- ZZ Specs
- · Replies 10 ·
Undergrad How to visualise bilinear form and inner products?
- mathmo94
- · Replies 3 ·
Graduate Why is the morphism to C an epimorphism in a short exact sequence?
- gentsagree
- · Replies 2 ·
Graduate Cosets: difference between these two statements
- ZZ Specs
- · Replies 2 ·
Graduate Do Orthogonal Subsets Spanning the Same Subspace Prove Equality?
- NATURE.M
- · Replies 4 ·
Graduate SVD Low-Rank Approximation Algorithm
- TheOldHag
- · Replies 8 ·
Prime ideals of K[X] where K is a field
- Math Amateur
- · Replies 1 ·
Graduate Why delete the origin from R³ to define the projective plane
- gentsagree
- · Replies 6 ·
Proving End($K^2$)=K for A-Module $K^2$
- Fermat1
- · Replies 7 ·
Graduate How Can I Publish My Beal Conjecture Findings?
- alberto4188
- · Replies 1 ·
Linear Dependency: Max Size of Subset of Vectors
- Yankel
- · Replies 2 ·
Graduate Is it possible to express all mathematics through atomic pieces of computation?
- tanus5
- · Replies 3 ·
Compute Ideal Generated by Matrix 3x3
- Fermat1
- · Replies 5 ·
Is \( A \) Isomorphic to \( \dfrac{R<X,Y>}{((X^2+1)X,(X^2+1)Y,YX)} \)?
- Fermat1
- · Replies 3 ·
Graduate Is the Laplace transform a group homomorphism or isomorphism?
- LagrangeEuler
- · Replies 7 ·
Algebra: Generating C as an R Algebra Subject to i^2=-1
- Fermat1
- · Replies 5 ·
Why is Sharp's Lemma 1.10 crucial for understanding R-algebras?
- Math Amateur
- · Replies 1 ·
Undergrad Linear algebra, when does the implications hold?
- bobby2k
- · Replies 3 ·
Maximal ideals of K[X] where K is a field
- Math Amateur
- · Replies 8 ·
Undergrad Multiple Choise Questions in Calculus/Algebra/Electromagnetism
- Magna Visus
- · Replies 2 ·
Number of elements and subgroups
- kalish1
- · Replies 1 ·
Graduate Why does the SVD low rank approximation still have full rank?
- TheOldHag
- · Replies 5 ·
Undergrad Are Matrix Multiplication Rules the Same for Composing Linear Transformations?
- 1MileCrash
- · Replies 3 ·
Matrix transform- about origin, then angular rotation
- Jundoe
- · Replies 4 ·
Graduate Are orthonormal eigenbases unique?
- Bipolarity
- · Replies 5 ·
What is the fastest method for computing determinants?
- Jundoe
- · Replies 10 ·
Graduate Set of invertible matrices with real entries
- LagrangeEuler
- · Replies 3 ·
Prove These 3 Statements About A Matrix: Rank of Adjoint
- Yankel
- · Replies 1 ·
Graduate Is $\mathcal{R}$ Lie Group Without 0?
- LagrangeEuler
- · Replies 11 ·
Is the Orthogonal Complement of an Invariant Subspace Itself Invariant?
- Sudharaka
- · Replies 2 ·
Undergrad Orthogonal Projections vs Non-orthogonal projections?
- rayzhu52
- · Replies 1 ·
Prove that every nonzero vector in V is a maximal vector for T.
- toni07
- · Replies 4 ·
Graduate Product of two Minkowksi metrics
- gentsagree
- · Replies 1 ·
Distance Between a Subspace and a Vector
- Sudharaka
- · Replies 2 ·
Undergrad Determinant of a unit columns matrix
- hedipaldi
- · Replies 7 ·
Graduate Left inverse of rectangular matrices when only right inverse exists
- genxium
- · Replies 10 ·
Distance from a vector to a subspace
- smile1
- · Replies 6 ·
High School Are orientation and direction the same thing for vectors?
- chemistry1
- · Replies 3 ·
Ideal structure for V = {(0,0), (1,1)} over F_2 in A^2
- Math Amateur
- · Replies 9 ·
What is the annihilator of a tensor in vector space V?
- Sudharaka
- · Replies 1 ·
Jordan Normal Form of Unitary Transformation
- Sudharaka
- · Replies 2 ·
Does a 4-dimensional subspace of 3×3 matrices always contain a symmetric matrix?
- Sudharaka
- · Replies 2 ·
Finding Basis of the Quotient Space
- Sudharaka
- · Replies 9 ·
Semigroup Structure: Exploiting Non-Finitely Generated Monoids
- mathbalarka
- · Replies 7 ·
Solving Systems of Linear Equations with ljx.m
- mathmari
- · Replies 1 ·
Undergrad Is the Matrix R Necessarily Lower Triangular in Matrix Decomposition?
- Jano L.
- · Replies 3 ·