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 Interpretation of direct product of Hilbert spaces
- IanBerkman
- · Replies 4 ·
Undergrad Coordinate System: Understanding Polar Vectors
- Devil Moo
- · Replies 8 ·
Graduate What Is the Spectrum of a Linear Operator in L2 Spaces?
- maxandri
- · Replies 2 ·
Converting right R-modules to left R-modules over noncommutative rings
- Math Amateur
- · Replies 3 ·
Undergrad Bland's split exact sequences vs Rotman's counterexample
- Math Amateur
- · Replies 12 ·
Proving λx = 0 implies λ = 0 when x ≠ 0 in division rings
- Math Amateur
- · Replies 2 ·
How Does Condition (2) Imply Condition (3) in Bland's Proposition 3.2.7?
- Math Amateur
- · Replies 36 ·
Undergrad Eigenvalue as a generalization of frequency
- npit
- · Replies 4 ·
Undergrad Proving Vector Space of Circles is Not Axiomatic
- mikeeey
- · Replies 2 ·
High School Polynomial Space: Can Degree 2 Fit in 1+x^2?
- mikeeey
- · Replies 1 ·
Finitely Cogenerated Modules - Bland Definition 4.1.3, Page 105
- Math Amateur
- · Replies 2 ·
Undergrad Question in linear algebra, derivation of a certain relation
- antonni
- · Replies 3 ·
Bland - Rings and their Modules 2011
- steenis
- · Replies 5 ·
High School Understanding Choi's Theorem and Notation in Matrix Theory
- naima
- · Replies 8 ·
Undergrad Why does the sine product operation give zero for non-parallel vectors?
- Devil Moo
- · Replies 9 ·
Each exact sequence can be arised by short exact sequences
- mathmari
- · Replies 2 ·
Exact Sequences and short exact sequences - basic question
- Math Amateur
- · Replies 5 ·
Graduate Hodge Dual as Sequence of Grade Reducing Steps
- MisterX
- · Replies 2 ·
Undergrad Simplifying 3 simultaneous equation into one equation
- Budana
- · Replies 10 ·
Undergrad Congruence vs equality in mod arithmetic
- jack476
- · Replies 3 ·
Graduate Rank 3x4 Complex Matrix Constraints
- swraman
- · Replies 3 ·
Undergrad Why is A.A = ||A||^2 in Vector Analysis?
- parshyaa
- · Replies 7 ·
Graduate Normalization and Scaling with Matrices
- doublee89
- · Replies 5 ·
Undergrad Solving equations with singular matrix
- Zak
- · Replies 2 ·
Undergrad Why vectors have components but scalar functions don't
- Frank Castle
- · Replies 16 ·
Undergrad Why must relations between group structures be functions?
- mikeeey
- · Replies 4 ·
Undergrad Difference between representations of SU2 and SU3
- Josh1079
- · Replies 5 ·
Undergrad Decomposing Vectors Using Row Reduction: A Practical Approach
- dman12
- · Replies 3 ·
Undergrad Why is the cross product perpendicular to both vectors?
- parshyaa
- · Replies 11 ·
Undergrad Tensor product and ultraproduct construction
- nomadreid
- · Replies 2 ·
Projective plane exercises 5(a) and 5(b) from Cox et al
- Math Amateur
- · Replies 1 ·
Undergrad Create an Equation for 3 Offspring Rabbits
- Dusto
- · Replies 2 ·
If irreducible p(x) and f(x) share root ρ, why does p(x) divide f(x)?
- mathmari
- · Replies 12 ·
High School Mistake when explaining associativity of vector addition
- CynicusRex
- · Replies 2 ·
Showing x² - y² = z² is a well-defined curve in ℙ²(ℝ)
- Math Amateur
- · Replies 2 ·
Insights Groups and Geometry - Comments
- micromass
- · Replies 7 ·
Graduate How Did They Derive Equation (49) from Equation (21) Using Matrix Identities?
- perplexabot
- · Replies 11 ·
Undergrad Parametric Representation of a Solution Set
- askor
- · Replies 1 ·
Exercise 1 from Cox et al chapter 8 on the projective plane
- Math Amateur
- · Replies 8 ·
Converting rational parametrization to homogeneous coordinates in P²
- Math Amateur
- · Replies 2 ·
Undergrad What angle to bevel pentagon edges for a plywood dodecahedron?
- arydberg
- · Replies 13 ·
Cox et al Exercise 8.1.3(a) - Projective plane
- Math Amateur
- · Replies 3 ·
High School Is the intersection of two planes a line?
- member 587159
- · Replies 9 ·
Undergrad Is Geometric Algebra inconsistent/circular?
- malawi_glenn
- · Replies 32 ·
Undergrad Conjugating a matrix in SL(2,ℝ) to an orthogonal matrix
- mnb96
- · Replies 9 ·
Graduate Cross product and rank 2 tensor determinant in exterior algebra
- MisterX
- · Replies 2 ·
Finding basis vectors for a solution space in ℝ⁴
- shamieh
- · Replies 1 ·
Algebraic element - Minimal polynomial
- mathmari
- · Replies 1 ·
Prime Subfield of Field F: Isomorphic to $\mathbb{Q}$
- evinda
- · Replies 1 ·
High School Sets and functions that gain more structure with context
- ProfuselyQuarky
- · Replies 9 ·
How to find a non-zero vector in the column space of M
- shamieh
- · Replies 1 ·
How can I find out if this matrix A's columns are linearly independent?
- shamieh
- · Replies 1 ·
Undergrad Dimension of the group O(n,R) - How to calc?
- JuanC97
- · Replies 3 ·
Undergrad Vector Division: An Explainer of Why It's Not Possible
- Atizaz Ahmed
- · Replies 5 ·
High School What Are Imaginary Numbers and How Can They Be Understood?
- Sobhan
- · Replies 11 ·
Undergrad Why is Φ a rotation given two vector images?
- Doradus
- · Replies 5 ·
Find all the matrices in Jordan form
- mathmari
- · Replies 19 ·
Wondering if $R$ is a P.I.D.: Free Modules and Ideals
- mathmari
- · Replies 6 ·
Proving <f₁, h> = <f₁, ..., fₛ> in Cox et al Chapter 1
- Math Amateur
- · Replies 3 ·
Is \(F[x]/<p(x)>\) the Root Field of \(x^4+ax^2+b\)?
- Kiwi1
- · Replies 1 ·
Undergrad Can two polynomials with GCF 1 share a common root?
- swampwiz
- · Replies 1 ·
Undergrad Matrix of columns of polynomials coefficients invertibility
- swampwiz
- · Replies 2 ·
Undergrad Algebraically Closed Fields
- Math Amateur
- · Replies 8 ·
High School Can a Binary Number be Viewed as an Orthogonal Basis?
- entropy1
- · Replies 2 ·
How Does Algebraic Closure Extend to Multivariable Polynomials?
- Math Amateur
- · Replies 2 ·
Exercise 3c on ideals in Q[x, y] from Cox, Little, O'Shea
- Math Amateur
- · Replies 2 ·
Affine Algebraic Sets in A^2 - Dummit and Foote, page 660, Example 3
- Math Amateur
- · Replies 2 ·
High School How Do You Compute the Expression E = AB - B^*A^* with Complex Numbers?
- TheCanadian
- · Replies 8 ·
Undergrad Eigenvalues and Eigenvectors question
- Dank2
- · Replies 16 ·
Show Im(gf)=Im(g) When f is Onto (Wondering)
- mathmari
- · Replies 4 ·
Undergrad How to determine if a subset of affine space is an algebraic set
- Math Amateur
- · Replies 3 ·
Graduate What is the state of the art in solving polynomial equations?
- jonjacson
- · Replies 15 ·
Undergrad Proving linear map with identity on W and negative identity on orthogonal complement
- Doradus
- · Replies 3 ·
Graduate Why Is the Discriminant Non-Positive in the Triangle Inequality Proof?
- LagrangeEuler
- · Replies 1 ·
Graduate What is an eigenframe?
- K41
- · Replies 6 ·
Undergrad SU(2) and su(2) have different dimensions?
- pellman
- · Replies 2 ·
Undergrad Affine Algebraic Sets - Dummit and Foote, page 660, Ex. 3
- Math Amateur
- · Replies 5 ·
Undergrad What is the Inverse of the Function f(x) = e^x + e^(-x) + 1?
- Eishan M
- · Replies 3 ·
Undergrad Prime elements: why define them only in integral domains?
- Math Amateur
- · Replies 20 ·
Undergrad Proving Identity for Determinant of $A^tA$
- tommyxu3
- · Replies 20 ·
Are D&F and Cooperstein's definitions of k-algebras equivalent?
- Math Amateur
- · Replies 2 ·
Undergrad K-algebra/associative algebra - equivalence of definitions
- Math Amateur
- · Replies 7 ·
Undergrad Polynomials in n indeterminates and UFDs
- Math Amateur
- · Replies 5 ·
Prime Elements in Non-Integral Domains?
- Math Amateur
- · Replies 1 ·
Statements about subrings and quotient
- mathmari
- · Replies 3 ·
Proof that K[X₁, X₂, ..., Xₙ] is a unique factorization domain
- Math Amateur
- · Replies 1 ·
Undergrad Difference between direct sum and direct product
- Silviu
- · Replies 1 ·
Undergrad Chladni plate with Neumann conditions
- Smollett
- · Replies 2 ·
High School Why is there a solution to this system?
- ProfuselyQuarky
- · Replies 15 ·
(x) and (x,y) are prime ideals of Q[x,y]
- mathmari
- · Replies 4 ·
Undergrad Tensor Products of Modules - Bland - Remark, Page 65
- Math Amateur
- · Replies 4 ·
Well-definedness of g in tensor product quotients (Bland)
- Math Amateur
- · Replies 1 ·
Free Z-module on M × N in Bland Proposition 2.3.3
- Math Amateur
- · Replies 3 ·
Bland's example on directly finite R-modules and M ≅ M ⊕ M
- Math Amateur
- · Replies 7 ·
Undergrad How Do Properties of Modulus Algebra Apply to RSA and Diffie-Hellman?
- FrankJ777
- · Replies 12 ·
These are the only submodule
- mathmari
- · Replies 12 ·
Undergrad Multiple time derivatives of gravitational potential
- Belginator
- · Replies 2 ·
Undergrad Spherical coordinates via a rotation matrix
- unicornflyers
- · Replies 3 ·
Undergrad What kind of space is the space of spinors?
- davi2686
- · Replies 4 ·
Undergrad Eigenspectra and Empirical Orthogonal Functions
- ecastro
- · Replies 4 ·