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.
Eigenstuff of Second Derivative
  • · Replies 4 ·
Replies
4
Views
2K
Pfaffian and determinants of skew symmetric matrices
  • · Replies 1 ·
Replies
1
Views
2K
Line operations on matrix products
  • · Replies 1 ·
Replies
1
Views
865
Are the Functions Linearly Independent Based on the Matrix of Their Outputs?
  • · Replies 2 ·
Replies
2
Views
1K
Line of intersection of two planes
  • · Replies 2 ·
Replies
2
Views
2K
Finding determinant through Gaussian elimination
  • · Replies 3 ·
Replies
3
Views
8K
Solving the Inversion Problem with RGB Filters
  • · Replies 1 ·
Replies
1
Views
1K
Is the Klein Four Group Identical to the Dihedral Group D2?
  • · Replies 3 ·
Replies
3
Views
2K
Associativity of Hadamard and matrix product
  • · Replies 2 ·
Replies
2
Views
2K
Length-Norm inequality to root-n times Length (using 2|uv| <= |u|^2 + |v|^2)
  • · Replies 4 ·
Replies
4
Views
1K
Why is det(C)=det(A)^(n-1) for cofactors and determinants?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Let F ={0 , 1 , a , b} be a field with four elements.
  • · Replies 2 ·
Replies
2
Views
3K
Proving Non-Trivial Solutions of Ax = b
  • · Replies 3 ·
Replies
3
Views
1K
Proving Determinant of Matrix Unchanged by Adding Columns
  • · Replies 2 ·
Replies
2
Views
5K
MHB Show that Q adjoin square roots of 2, 3 is a vector space of dimension 4 over Q
  • · Replies 1 ·
Replies
1
Views
2K
Groups of homomorphisms of abelian groups
  • · Replies 1 ·
Replies
1
Views
2K
MHB Showing that $A$ is an Ideal of $\mathbb{Q}[x]$ and Expressing it as $<f(x)>$
  • · Replies 4 ·
Replies
4
Views
2K
Is intuition more important than logical proof in mathematics?
  • · Replies 7 ·
Replies
7
Views
4K
Can you explain the determinant formula using permutation notation?
  • · Replies 3 ·
Replies
3
Views
8K
MHB Every submodule has at least one set of generators?
  • · Replies 7 ·
Replies
7
Views
2K
Does the inverse of this special matrix have a power series expansion?
  • · Replies 5 ·
Replies
5
Views
1K
Is the Canonical Basis in Mathematics Just a Useful Convention?
  • · Replies 6 ·
Replies
6
Views
6K
Properties of Kernels of Homeomorphisms
  • · Replies 7 ·
Replies
7
Views
1K
MHB What is the Proof for the Nonempty Intersection of Submodules Being a Submodule?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Why must the ring $K[x]$ have infinitely many irreducible polynomials?
  • · Replies 7 ·
Replies
7
Views
2K
Transform Cylindrical coordinates into Cartesian Coordiantes
  • · Replies 3 ·
Replies
3
Views
2K
MHB The polynomial is irreducible iff the condition is satisfied
  • · Replies 3 ·
Replies
3
Views
2K
Explicit construction of isomorphisms of low-rank Lie algebras.
  • · Replies 2 ·
Replies
2
Views
5K
MHB Problem Regarding Left Unital Artinian Ring (set by Euge)
  • · Replies 3 ·
Replies
3
Views
1K
MHB Field extension-degree of the minimal polynom
  • · Replies 1 ·
Replies
1
Views
1K
MHB Ordered Index Sets for Direct Sums & Products of Modules: Explained by B&K
  • · Replies 7 ·
Replies
7
Views
2K
MHB Direct Sums of Copies of Modules - B&K - Exercise 2.1.6 (iii)
  • · Replies 7 ·
Replies
7
Views
2K
MHB Show the Units of Zn with modular multiplication are a group
  • · Replies 2 ·
Replies
2
Views
2K
MHB Finding Notation for Left Invariant Vector Fields on Lie Groups
  • · Replies 3 ·
Replies
3
Views
2K
Function scales eigenvalues, but what happens to eigenvectors?
  • · Replies 7 ·
Replies
7
Views
2K
Finding Inverse of Matrix by using Gaussian-Jordan Elimination
  • · Replies 6 ·
Replies
6
Views
5K
MHB Definition of a Right Artinian Ring - Cohn - page 66
  • · Replies 15 ·
Replies
15
Views
4K
MHB Free modules, M_n(R)-modules and M_N(R)-R-bimodules - Berrick and Keating
  • · Replies 1 ·
Replies
1
Views
1K
MHB Infinite Direct Sums and Standard Inclusions and Projections
  • · Replies 1 ·
Replies
1
Views
1K
MHB Direct Products and External Direct Sums
  • · Replies 2 ·
Replies
2
Views
3K
Question about invariant w.r.t. a group action
  • · Replies 3 ·
Replies
3
Views
2K
Understanding Linear Algebra Solutions: Sketching and Ratios Explained
  • · Replies 3 ·
Replies
3
Views
2K
MHB Determining if a set is a subspace.
  • · Replies 4 ·
Replies
4
Views
4K
MHB Proof: $K[a]$ is a Field & if $K(a)=K[a]$, then $a$ is Algebraic Over $K$
  • · Replies 2 ·
Replies
2
Views
2K
MHB What Determines Group Homomorphisms Between Rational Numbers?
  • · Replies 5 ·
Replies
5
Views
4K
MHB Modules of Finite Length - Cohn, page 61
  • · Replies 34 ·
2
Replies
34
Views
5K
MHB Generalizing Rigid Motions Group w/ Metric
  • · Replies 3 ·
Replies
3
Views
2K
MHB What is the Definition of a Derivation for a Lie Algebra?
  • · Replies 4 ·
Replies
4
Views
2K
Proof of R being a Vector Space - Best Resources Available
  • · Replies 7 ·
Replies
7
Views
1K
SU(2) as a normal subgroup of SL(2, C)
  • · Replies 3 ·
Replies
3
Views
2K
MHB Definition of SO(n): O(n) & SL(n, \mathbb{R}) Intersection
  • · Replies 1 ·
Replies
1
Views
2K
Writing 3rd Order Tensor Symmetric Part in Tensor Form
  • · Replies 5 ·
Replies
5
Views
2K
Are All Indecomposable Groups Cyclic?
  • · Replies 4 ·
Replies
4
Views
2K
Is simultaneous row operation allowed in reducing a matrix to row echelon form?
  • · Replies 5 ·
Replies
5
Views
2K
Why Does a Functional Depend on the Curve and Its Derivative?
  • · Replies 1 ·
Replies
1
Views
1K
Show that origin in R^n is the n-tuple 0=(0,0, .,0)
  • · Replies 6 ·
Replies
6
Views
1K
MHB A group of even order contains an odd number of elements of order 2
  • · Replies 3 ·
Replies
3
Views
4K
MHB Looking for an online Algebra resource
  • · Replies 6 ·
Replies
6
Views
2K
MHB Subnormal Series and Composition Series
  • · Replies 6 ·
Replies
6
Views
2K
MHB Theorem on the Lengths of Modules - Cohn, Theorem 2.5
  • · Replies 1 ·
Replies
1
Views
1K
What are the algebra prerequisites for Lie groups?
  • · Replies 24 ·
Replies
24
Views
6K
MHB Show that the elements have the same order
  • · Replies 5 ·
Replies
5
Views
1K
MHB Verifying Sentences about Groups: Answers and Hints
  • · Replies 6 ·
Replies
6
Views
2K
MHB Help Peter Prove Simple Proposition on Simple Groups & Maximal Normal Subgroups
  • · Replies 3 ·
Replies
3
Views
2K
MHB Factor Groups and Simple Groups - Fraleigh: Theorem 15.18
  • · Replies 1 ·
Replies
1
Views
2K
MHB Show that there are y,z such that y,z commute and their order is m and n
  • · Replies 2 ·
Replies
2
Views
1K
MHB A cyclic group with only one generator can have at most two elements
  • · Replies 4 ·
Replies
4
Views
3K
MHB Vector algebra- centroid of tetrahedron
  • · Replies 3 ·
Replies
3
Views
6K
Solving Doubts When Showing Simple Properties of Norms
  • · Replies 7 ·
Replies
7
Views
2K
MHB Proof that covariance matrix is positive semidefinite
  • · Replies 1 ·
Replies
1
Views
9K
Finding intersection of three planes
  • · Replies 5 ·
Replies
5
Views
2K
Any1 can recommend any good e-book for linear algebra ?
  • · Replies 5 ·
Replies
5
Views
1K
Possible title: When Does the Kernel of a Homomorphism Reduce to the Identity?
  • · Replies 5 ·
Replies
5
Views
2K
Solutions to Span of Functions Problems
  • · Replies 3 ·
Replies
3
Views
4K
MHB Definitions of Algebras in Cohn and in Golan
  • · Replies 8 ·
Replies
8
Views
2K
Symmetric Tensor Product in Pic. 1 - Explained
  • · Replies 2 ·
Replies
2
Views
1K
MHB Solving Linear Transformations with Matrix A and Vectors u1 & u2
  • · Replies 4 ·
Replies
4
Views
3K
Transform 10 to 1000 Points on x^9 to x^2 Polynomial
  • · Replies 7 ·
Replies
7
Views
2K
MHB Definitions of Algebras in Cohn and in Dummit and Foote
  • · Replies 10 ·
Replies
10
Views
3K
MHB Second Isomorphism Theorem for Groups
  • · Replies 8 ·
Replies
8
Views
2K
Definition Of Operator Exponential?
  • · Replies 3 ·
Replies
3
Views
3K
MHB First Isomorphism Theorem for Modules - Cohn Theorem 1.17
  • · Replies 12 ·
Replies
12
Views
3K
MHB Quotient Modules and Module Homomorphisms - Cohn - Corollary 1.16
  • · Replies 6 ·
Replies
6
Views
2K
Rules for Multiplying and Adding in Modulo # Calculation
  • · Replies 4 ·
Replies
4
Views
2K
Relationship between linear (in)dependency and span
  • · Replies 5 ·
Replies
5
Views
4K
MHB Quotient Modules and Homomorphisms
  • · Replies 3 ·
Replies
3
Views
1K
MHB Modules in Cohn's book on ring theory - simple notational issue
  • · Replies 23 ·
Replies
23
Views
4K
MHB Need help understanding a Lie Algebra
  • · Replies 7 ·
Replies
7
Views
2K
Self-adjoint operators and Hermitian operators
  • · Replies 4 ·
Replies
4
Views
4K
Factorizing ##F_{ab}(M)## w/ Respect to Grothendieck Group - Lang's Book
  • · Replies 5 ·
Replies
5
Views
2K
Linear Algebra Help: Reduce Matrix & Find Error
  • · Replies 4 ·
Replies
4
Views
2K
MHB Finitely Generated Modules and Ascending Chains
  • · Replies 11 ·
Replies
11
Views
3K
Number of quadratic residues mod N>1
  • · Replies 3 ·
Replies
3
Views
4K
MHB Chains of Modules and Composition Series
  • · Replies 3 ·
Replies
3
Views
2K
Non-square linear systems with exterior product
  • · Replies 1 ·
Replies
1
Views
2K
Linear operators and vector spaces
  • · Replies 5 ·
Replies
5
Views
2K
MHB Noetherian Modules - Cohn Theorem 2.2
  • · Replies 4 ·
Replies
4
Views
2K
MHB Noetherian Modules and Finitely Generated Modules
  • · Replies 2 ·
Replies
2
Views
1K
MHB Are rationals adjoin cube root of 3 a field?
  • · Replies 3 ·
Replies
3
Views
6K
MHB You're welcome, Peter! I'm glad it was helpful.
  • · Replies 2 ·
Replies
2
Views
2K