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 Introduction to linear and abstract algebra
- TheBiologist
- · Replies 8 ·
Graduate Are There Spaces That Are Their Own Automorphisms Group?
- TrickyDicky
- · Replies 4 ·
Calculate Resultant of $g(x)=X^3+pX+q$
- evinda
- · Replies 5 ·
Showing $XF_{X}+YF_{Y}+ZF_{Z}=nF$ with a Homogeneous Polynomial
- evinda
- · Replies 4 ·
The Contravariant Functor Hom_R( _ , X)
- Math Amateur
- · Replies 2 ·
Composition Series for Group Order 30
- Pratibha
- · Replies 4 ·
Graduate 3 Dimensional Representation of D3
- ChrisVer
- · Replies 2 ·
Irreducible polynomial/Splitting field
- mathmari
- · Replies 3 ·
Short Five Lemma - Checking Some Simple 'Diagram Chasing'
- Math Amateur
- · Replies 2 ·
Undergrad Basic Questions in linear algebra and group theory
- Heisenberg1993
- · Replies 8 ·
Simple Issue of oh symbol - exact sequences
- Math Amateur
- · Replies 2 ·
Graduate Momentum operator in "open" space
- ShayanJ
- · Replies 3 ·
Bilinear Form Non-Degenerate on a Subspace.
- caffeinemachine
- · Replies 5 ·
The equation has exactly m different solutions
- mathmari
- · Replies 1 ·
Undergrad Linearly Independent Sets and Spans in R4
- grassstrip1
- · Replies 1 ·
Undergrad Quaternion smoothing with exponential moving average causing incorrect rotations
- twoski
- · Replies 15 ·
Graduate Why use the notation (s, a, b, c) for quaternions instead of (s, v)?
- Septimra
- · Replies 1 ·
Graduate Why Cardano's method gives 6 solutions for z but only 3 distinct cubic roots
- PcumP_Ravenclaw
- · Replies 1 ·
Graduate A Large scale eigenvalue problem solver
- jollage
- · Replies 5 ·
Split Short Exact Sequences - Bland - Proposition 3.2.6
- Math Amateur
- · Replies 2 ·
How Do We Find the Embeddings of $\mathbb{Q}(\sqrt{2})$ in $\mathbb{R}$?
- mathmari
- · Replies 1 ·
Proving V(sum of ideals) equals intersection of varieties
- evinda
- · Replies 13 ·
Show Irreducibility of $K^n$ Algebraic Set $V$ iff $I(V)$ is a Prime Ideal
- evinda
- · Replies 13 ·
Undergrad Does the column space basis span the same subspace as the row space basis?
- PsychonautQQ
- · Replies 2 ·
Graduate Adjacency matrices: (a) notation discrepancy, and (b) applications
- nomadreid
- · Replies 3 ·
Are the Fields $\mathbb{F}_{2^2}$ and $\mathbb{Z}_2(a)$ Equal?
- mathmari
- · Replies 2 ·
Graduate Isomorphism between Clifford algebras CL(4,2) and CL(2,4)
- mnb96
- · Replies 4 ·
Initial objects in Set category and functions from empty set
- Math Amateur
- · Replies 4 ·
Undergrad Can a One-Sided Identity Element in Groups Lead to Two-Sided Identity?
- HyperActive
- · Replies 5 ·
Interpreting morphism notation in category of matrices over a ring
- Math Amateur
- · Replies 2 ·
Undergrad Division Algorithm for Polynomials in R[x] confusing me
- PsychonautQQ
- · Replies 1 ·
Showcasing $V(I \cap J)=V(I) \cup V(J)$ in Polynomials
- evinda
- · Replies 1 ·
Graduate Roots of unity, Roots of complex equations of the form z^n = 1
- PcumP_Ravenclaw
- · Replies 2 ·
Undergrad Nonhomogeneous System: Similar Coefficients & Solutions?
- kosovo dave
- · Replies 5 ·
Graduate Confusion about position operator in QM
- ShayanJ
- · Replies 1 ·
Finding price from a demand function with negative result
- GangsterWaffle
- · Replies 1 ·
Graduate Number of eigenvectors for Hermitian matrices
- haisydinh
- · Replies 6 ·
Graduate How do I rotate an inertia tensor in Cartesian coordinates?
- bugatti79
- · Replies 4 ·
Undergrad Is the Matrix B Positive or Not?
- nomadreid
- · Replies 3 ·
Undergrad Does E*A*E^(-1) equal E^(-1)*A*E for matrices?
- Woolyabyss
- · Replies 1 ·
Graduate Free Modules: Bland Corollary 2.2.4 - Issue on Finite Generation
- Math Amateur
- · Replies 1 ·
Graduate Rotation isometry on the complex plane derivation
- PcumP_Ravenclaw
- · Replies 3 ·
Problem with idempotent matrices
- Samme013
- · Replies 5 ·
Commutative rings are IBN-rings - Bland Proposition 2.2.11
- Math Amateur
- · Replies 4 ·
Why construct intermediate bases in Bland's IBN-ring proof
- Math Amateur
- · Replies 1 ·
Free Modules With More Than One Basis - Bland - Example 5, page 56
- Math Amateur
- · Replies 5 ·
Graduate Lie Groups, Lie Algebra and Vectorfields
- JonnyMaddox
- · Replies 3 ·
Free Modules w/Multiple Bases: 2nd Issue w/Example 5 (Paul E. Bland)
- Math Amateur
- · Replies 1 ·
Notation for the standard free right R-module Fr_R(X)
- Math Amateur
- · Replies 15 ·
Is $C[x,y,z]/<y-x^2,z-x^3>$ an Integral Domain?
- evinda
- · Replies 1 ·
Graduate Solving Cyclic Group Questions: How Many Elements of Order What?
- jimmycricket
- · Replies 2 ·
Graduate Our Old Friend, the Twin Primes Conjecture
- tuttlerice
- · Replies 11 ·
Endomorphism Rings - Bland Example 7 - page 10
- Math Amateur
- · Replies 1 ·
Free Modules - Bland - Proposition 2.2.3
- Math Amateur
- · Replies 5 ·
Graduate Is every diagonalizable representation of a group reducible?
- Faust90
- · Replies 10 ·
Graduate Proof of the twin primes conjecture
- StatGuy2000
- · Replies 3 ·
Free Modules: Solving Issue of Finite Generation Corollary 2.2.4
- Math Amateur
- · Replies 3 ·
Why does an isomorphism f: R^(Δ) → F with f(eα) = xα imply {xα}Δ is a basis?
- Math Amateur
- · Replies 1 ·
Undergrad Do Row Operations Maintain Equivalence in Matrix Subtraction?
- MathewsMD
- · Replies 5 ·
Undergrad Duality and Orthogonality: What's the Difference?
- janu203
- · Replies 6 ·
Graduate Projection of a on b when a, b are complex
- johann1301
- · Replies 2 ·
Graduate Derivation of rotation isometry on the complex plane
- PcumP_Ravenclaw
- · Replies 2 ·
Quadratic form, determine the surface
- vincentvance
- · Replies 1 ·
Bland Proposition 2.2.3 proof: why almost all coefficients are zero
- Math Amateur
- · Replies 1 ·
Graduate The adjoint representation of a semisimple Lie algebra is completely reducible
- maverick280857
- · Replies 4 ·
Prime ideal generated by Y-X² and Z-X³
- evinda
- · Replies 1 ·
Graduate Some questions about group representations
- ShayanJ
- · Replies 7 ·
Proving Maximal Ideal of $\mathbb{C}[X,Y]$
- evinda
- · Replies 12 ·
Simple Issue with Submodules - Northcott, Proposition 2, pages 7-8
- Math Amateur
- · Replies 2 ·
Sum of an Indexed Family of Submodules - Northcott, pages 8-9
- Math Amateur
- · Replies 1 ·
Graduate Is the Direct Product of Two Finite Cyclic Groups Cyclic
- Bashyboy
- · Replies 7 ·
Question on rank-nullity theorem
- SarahER
- · Replies 2 ·
Undergrad Zero Dimensional Null Space (What's the meaning of this?)
- kosovo dave
- · Replies 4 ·
Graduate How do you take a tensor product?
- space-time
- · Replies 5 ·
How to solve the following matrix rotation
- Logan Land
- · Replies 5 ·
High School Definition of determinant for 2x2 matrix
- MathewsMD
- · Replies 2 ·
Finding the Rank and Basis for a matrix
- Logan Land
- · Replies 3 ·
Finding a 3×2 matrix from a given formula for entries
- leprofece
- · Replies 1 ·
Undergrad Difference between orthogonal transformation and linear transformation
- EnglsihLearner
- · Replies 9 ·
Why is the characteristic different from 2?
- evinda
- · Replies 2 ·
Undergrad Possible Number of Vertices for Graphs with Three Edge Connections
- metapuff
- · Replies 4 ·
Graduate Relating D_4 notation with rotations and reflections
- Bashyboy
- · Replies 3 ·
Undergrad Why verify vector space axioms if they seem like basic properties
- MarcL
- · Replies 2 ·
Undergrad Linear algebra exam problems: vector spaces and matrices
- KevinCT
- · Replies 1 ·
Find matrix A where aij = (∛2)^i + (-4)^j·√3
- leprofece
- · Replies 1 ·
Surjectivity of a Free Module Homomorphism implies injectivity
- caffeinemachine
- · Replies 3 ·
Graduate Proof of Left Cosets Partition a Group
- Bashyboy
- · Replies 5 ·
Graduate Are the Only Ideals in M(2, R) Trivial?
- WWGD
- · Replies 3 ·
External and Internal Direct Sums - Bland - Rings and Their Modules
- Math Amateur
- · Replies 2 ·
Undergrad Proving vectors are in the column space
- Taylorw369
- · Replies 3 ·
Graduate How can Lambert's equation be used to solve for x?
- psyclone
- · Replies 2 ·
Undergrad For G = <a: a^100 = e>, find the following
- CoachBryan
- · Replies 1 ·
Graduate Solving Computations w/ Cycles: Permutations, Inverses, Orders
- CoachBryan
- · Replies 5 ·
Problem about a group with two inner direct product representations
- stragequark
- · Replies 3 ·
Meaning of a/p notation in integral domains without inverses
- Math Amateur
- · Replies 1 ·
Graduate Proof of Trace Orthogonality Relation for Matrices $\Gamma^A$
- gentsagree
- · Replies 1 ·
Find basis and dimension of the intersection of S and T
- Logan Land
- · Replies 17 ·
Find the image of a two variable function
- Synapse0x
- · Replies 3 ·
Is it true these are theorems in Linear Algebra?
- Logan Land
- · Replies 2 ·
Undergrad Algebra experiment using cellophane
- srfriggen
- · Replies 4 ·