Linear and Abstract Algebra Forum

Post thread
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.
MHB Short Five Lemma - Checking Some Simple 'Diagram Chasing'
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Basic Questions in linear algebra and group theory
  • · Replies 8 ·
Replies
8
Views
2K
MHB Simple Issue of oh symbol - exact sequences
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Momentum operator in "open" space
  • · Replies 3 ·
Replies
3
Views
1K
MHB Bilinear Form Non-Degenerate on a Subspace.
  • · Replies 5 ·
Replies
5
Views
3K
MHB The equation has exactly m different solutions
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Linearly Independent Sets and Spans in R4
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Can anyone help me fix quaternion rotation errors in Unity?
  • · Replies 15 ·
Replies
15
Views
4K
Graduate Why use the notation (s, a, b, c) for quaternions instead of (s, v)?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Understanding the method to solve the cubic equation
  • · Replies 1 ·
Replies
1
Views
2K
Graduate A Large scale eigenvalue problem solver
  • · Replies 5 ·
Replies
5
Views
3K
MHB Split Short Exact Sequences - Bland - Proposition 3.2.6
  • · Replies 2 ·
Replies
2
Views
1K
MHB How Do We Find the Embeddings of $\mathbb{Q}(\sqrt{2})$ in $\mathbb{R}$?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Proving Intersection of Ideals in $K[x_1,x_2,...,x_n]$
  • · Replies 13 ·
Replies
13
Views
3K
MHB Show Irreducibility of $K^n$ Algebraic Set $V$ iff $I(V)$ is a Prime Ideal
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Question about row space basis and Column space basis
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Adjacency matrices: (a) notation discrepancy, and (b) applications
  • · Replies 3 ·
Replies
3
Views
2K
MHB Are the Fields $\mathbb{F}_{2^2}$ and $\mathbb{Z}_2(a)$ Equal?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Isomorphism between Clifford algebras CL(4,2) and CL(2,4)
  • · Replies 4 ·
Replies
4
Views
2K
MHB Categories - Bland Chapter 3 - Problem 2 - Problem Set 3.1
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Can a One-Sided Identity Element in Groups Lead to Two-Sided Identity?
  • · Replies 5 ·
Replies
5
Views
3K
MHB Categories - Bland Chapter 3 - Problem 1 - Problem Set 3.1
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Division Algorithm for Polynomials in R[x] confusing me
  • · Replies 1 ·
Replies
1
Views
2K
MHB Showcasing $V(I \cap J)=V(I) \cup V(J)$ in Polynomials
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Roots of unity, Roots of complex equations of the form z^n = 1
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Nonhomogeneous System: Similar Coefficients & Solutions?
  • · Replies 5 ·
Replies
5
Views
1K
Graduate Confusion about position operator in QM
  • · Replies 1 ·
Replies
1
Views
982
MHB Solving Supply & Demand Equations - Get the Price You Need!
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Number of eigenvectors for Hermitian matrices
  • · Replies 6 ·
Replies
6
Views
2K
Graduate How do I rotate an inertia tensor in Cartesian coordinates?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Is the Matrix B Positive or Not?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Do Matrix Inverses Commute When Flanking Another Matrix?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Free Modules: Bland Corollary 2.2.4 - Issue on Finite Generation
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Doubt about rotation isometry on the complex plane
  • · Replies 3 ·
Replies
3
Views
2K
MHB Problem with idempotent matrices
  • · Replies 5 ·
Replies
5
Views
2K
MHB Commutative rings are IBN-rings - Bland Proposition 2.2.11
  • · Replies 4 ·
Replies
4
Views
2K
MHB Help with Paul E. Bland's Division Rings and IBN-rings Prop 2.2.10 Proof
  • · Replies 1 ·
Replies
1
Views
1K
MHB Free Modules With More Than One Basis - Bland - Example 5, page 56
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Lie Groups, Lie Algebra and Vectorfields
  • · Replies 3 ·
Replies
3
Views
2K
MHB Free Modules w/Multiple Bases: 2nd Issue w/Example 5 (Paul E. Bland)
  • · Replies 1 ·
Replies
1
Views
1K
MHB Understanding the Standard Free Right Module on a Set X?
  • · Replies 15 ·
Replies
15
Views
3K
MHB Is $C[x,y,z]/<y-x^2,z-x^3>$ an Integral Domain?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Solving Cyclic Group Questions: How Many Elements of Order What?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Our Old Friend, the Twin Primes Conjecture
  • · Replies 11 ·
Replies
11
Views
2K
MHB Endomorphism Rings - Bland Example 7 - page 10
  • · Replies 1 ·
Replies
1
Views
1K
MHB Free Modules - Bland - Proposition 2.2.3
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Is every diagonalizable representation of a group reducible?
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Proof of the twin primes conjecture
  • · Replies 3 ·
Replies
3
Views
3K
MHB Free Modules: Solving Issue of Finite Generation Corollary 2.2.4
  • · Replies 3 ·
Replies
3
Views
2K
MHB Free Modules - Another issue regarding Bland Proposition 2.2.4
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Do Row Operations Maintain Equivalence in Matrix Subtraction?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Duality and Orthogonality: What's the Difference?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Projection of a on b when a, b are complex
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Derivation of rotation isometry on the complex plane
  • · Replies 2 ·
Replies
2
Views
1K
MHB Quadratic form, determine the surface
  • · Replies 1 ·
Replies
1
Views
2K
MHB Free Modules - Another problem regarding Bland Proposition 2.2.3
  • · Replies 1 ·
Replies
1
Views
1K
Graduate The adjoint representation of a semisimple Lie algebra is completely reducible
  • · Replies 4 ·
Replies
4
Views
2K
MHB Exploring Algebraic Sets: Finding Irreducibility and Prime Ideals
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Some questions about group representations
  • · Replies 7 ·
Replies
7
Views
2K
MHB Proving Maximal Ideal of $\mathbb{C}[X,Y]$
  • · Replies 12 ·
Replies
12
Views
3K
MHB Simple Issue with Submodules - Northcott, Proposition 2, pages 7-8
  • · Replies 2 ·
Replies
2
Views
1K
MHB Sum of an Indexed Family of Submodules - Northcott, pages 8-9
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is the Direct Product of Two Finite Cyclic Groups Cyclic
  • · Replies 7 ·
Replies
7
Views
3K
MHB Question on rank-nullity theorem
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Zero Dimensional Null Space (What's the meaning of this?)
  • · Replies 4 ·
Replies
4
Views
16K
Graduate How do you take a tensor product?
  • · Replies 5 ·
Replies
5
Views
2K
MHB How to solve the following matrix rotation
  • · Replies 5 ·
Replies
5
Views
3K
High School Definition of determinant for 2x2 matrix
  • · Replies 2 ·
Replies
2
Views
2K
MHB Finding the Rank and Basis for a matrix
  • · Replies 3 ·
Replies
3
Views
2K
MHB SEO) Discovering Matrix 2: A 3x2 Matrix Calculation and Its Applications
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Difference between orthogonal transformation and linear transformation
  • · Replies 9 ·
Replies
9
Views
7K
MHB Why is the characteristic different from 2?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Possible Number of Vertices for Graphs with Three Edge Connections
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Dihedral Group D_4: Denotations & Correspondence
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Some help understanding vector space
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Need help with some linear algebra questions
  • · Replies 1 ·
Replies
1
Views
906
MHB Finding the Matrix Aij: Cubic Root of 2, -4 Power of j & Sqrt of 3)
  • · Replies 1 ·
Replies
1
Views
1K
MHB Surjectivity of a Free Module Homomorphism implies injectivity
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Proof of Left Cosets Partition a Group
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Are the Only Ideals in M(2, R) Trivial?
  • · Replies 3 ·
Replies
3
Views
2K
MHB External and Internal Direct Sums - Bland - Rings and Their Modules
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Proving vectors are in the column space
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How can Lambert's equation be used to solve for x?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad For G = <a: a^100 = e>, find the following
  • · Replies 1 ·
Replies
1
Views
852
Graduate Solving Computations w/ Cycles: Permutations, Inverses, Orders
  • · Replies 5 ·
Replies
5
Views
2K
MHB Problem about a group with two inner direct product representations
  • · Replies 3 ·
Replies
3
Views
2K
MHB Elements of the form a/b in an integral domain - simple question
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Proof of Trace Orthogonality Relation for Matrices $\Gamma^A$
  • · Replies 1 ·
Replies
1
Views
1K
MHB Find basis and dimension of the intersection of S and T
  • · Replies 17 ·
Replies
17
Views
5K
MHB Find the image of a two variable function
  • · Replies 3 ·
Replies
3
Views
2K
MHB Is it true these are theorems in Linear Algebra?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Algebra experiment using cellophane
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Linear Algebra Matrix Transformation to plane
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Row and Column equivalent matrices
  • · Replies 4 ·
Replies
4
Views
8K
MHB Modules - Northott: Proposition 1
  • · Replies 2 ·
Replies
2
Views
1K
MHB Show that it satisfies the equation
  • · Replies 12 ·
Replies
12
Views
3K
MHB Show $\|.\|$ is an Norm: Prove Triangle Inequality
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Factor Groups: What am I thinking about wrongly here?
  • · Replies 3 ·
Replies
3
Views
1K
MHB Algebraic Proofs and Verifying identities
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Is Matrix Addition Commutative?
  • · Replies 4 ·
Replies
4
Views
2K