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.
Graduate Existence of Singer Cycle in GL(n,q)
  • · Replies 13 ·
Replies
13
Views
6K
Graduate Characteristic polynomial splits into linear factors
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Addition Table for Z2 & Prove if G is Abelian
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Proving A and B Finite Sets: Injectivity and Surjectivity of f:A->B
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Are There Really TWO New Mersenne Primes Bigger Than 10M Digits?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Is the Is Reachable From Relation an Equivalence Relation in Directed Graphs?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Is a Full Binary Tree's Internal Path Length Equal to Its External Path Length?
  • · Replies 1 ·
Replies
1
Views
7K
Graduate Normal subgroups and Abelian property
  • · Replies 3 ·
Replies
3
Views
8K
Undergrad The logic behind the cross product with units
  • · Replies 1 ·
Replies
1
Views
16K
Graduate Prove that if h is in H, then also h^-1
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How Do You Calculate the Probability of a Rat Being in Room 4 After Two Moves?
  • · Replies 2 ·
Replies
2
Views
9K
High School The vector resolute.Why doesn't it cancel out?
  • · Replies 2 ·
Replies
2
Views
4K
High School What is the Expression for the Difference of Two Square Numbers?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Finding a polynomial when only given five points
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Name of Norm-preserving Linear Transformations?
  • · Replies 2 ·
Replies
2
Views
3K
High School Is there any general formula for strings?
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Proving the Primality of a Polynomial over Finite Fields
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is Partial Trace Cyclic for Density Matrices in Quantum Systems?
  • · Replies 3 ·
Replies
3
Views
6K
Graduate Elements of Subgroups in Additive Group Q/Z: G(2) and G(P)
  • · Replies 1 ·
Replies
1
Views
10K
Undergrad Is there a pattern to the values of k for which 10^k+1 is divisible by a square?
  • · Replies 27 ·
Replies
27
Views
13K
Undergrad Binomial theorum, when k is a multiple of x
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Seeking a Proof of Incommensurability
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad # of different binary ops. on a set S
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Find Order of Elements & Matrices: A Comprehensive Guide
  • · Replies 2 ·
Replies
2
Views
20K
Graduate Is my method for finding the dual in Dirac notation correct?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad A number of 10 digits is build up in the following way
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Why do we need generalized eigenvectors for matrices with repeated eigenvalues?
  • · Replies 10 ·
Replies
10
Views
5K
Graduate Proving Incommensurability in Number Theory with a Graph
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad What are the real-world applications of linear algebra?
  • · Replies 39 ·
2
Replies
39
Views
35K
Graduate Proving Projective Modules Have Free Modules as Direct Sums
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Primality proving for 'near-powers'
  • · Replies 4 ·
Replies
4
Views
2K
Graduate A question of fully invariant subgroup
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Check my work (Spivak problem in Calculus on Manifolds)
  • · Replies 18 ·
Replies
18
Views
5K
Graduate Is A Skew Symmetric?
  • · Replies 5 ·
Replies
5
Views
7K
Graduate Basic Group Theory: Proof <A,B>n<C>=<AuBnC>
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Evaluating the Riemann Zeta Function: Step-by-Step Guide for \zeta(c + xi)
  • · Replies 12 ·
Replies
12
Views
6K
Graduate Eigenvalue Problem: Directional Loss & Consequences
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Unsigned Stirling numbers of the first kind
  • · Replies 2 ·
Replies
2
Views
5K
Undergrad Is n^2 congruent to 0 or 1 (mod 3) for any integer n?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Derivation of nth fibonacci term
  • · Replies 11 ·
Replies
11
Views
30K
Graduate Weak form of Dirichlet's theorem
  • · Replies 12 ·
Replies
12
Views
4K
Graduate Does least squares regularization have to be iterative?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Transforming a 4x4 matrix from one base to another
  • · Replies 3 ·
Replies
3
Views
6K
Where Does Group Theory Belong on Physics Forums?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Group Theory - Help in learning
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Solving U, V, W Subspaces Problem
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Simultaneous Equation with 4 variables, can it be don?
  • · Replies 9 ·
Replies
9
Views
10K
Graduate Is x^{\sqrt{5}}=y for Rational Numbers?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Understanding Strongly Nilpotent Elements
  • · Replies 1 ·
Replies
1
Views
3K
Graduate A simple domain not being skew field?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Herstein, Topics in Algebra, page 58
  • · Replies 6 ·
Replies
6
Views
13K
Graduate Prove Simplicity of R-Module V & Find Jac(R) & isomorphism R + R
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is it Possible to Embed F/R into F without Complementation?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad An inquiry into whether or not 1000009 is a prime number
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Is Z[T]/(T^3) a Field Due to T^3's Irreducibility?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Integers. I on this one please?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Three corollaries to a well-known theorem
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Rank of a Matrix: Can We Eliminate Lines to Get Non-Vanishing Determinant?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad What Is the Difference Between Isomorphisms and Homomorphisms?
  • · Replies 11 ·
Replies
11
Views
13K
Undergrad Do A/<b(x)> and A/<c(x)> have the same number of elements?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Isomorphic groups that have different properties?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Is it possible to find function that describes irrational things?
  • · Replies 20 ·
Replies
20
Views
6K
Graduate Irreducible polynomials over finite fields
  • · Replies 15 ·
Replies
15
Views
16K
Undergrad Finding Roots of Irreducible Polynomials in Z5
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Determinate of a Matrix of any (square) order
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Integers reachable by ax + by + 30xy
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Eigenvalue question, hermitian matrix
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Finding the Number of Primitive Polynomials in Finite Fields
  • · Replies 25 ·
Replies
25
Views
11K
Undergrad Suggest any titles that i could research?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Spreading vectors around an area
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Solving Optimization Problem: Local Minima Traps & Solutions
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is the Solution for Problem 2 on the Algebra Qualifier Exam Correct?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Proving Polynomial Properties: Existence of nxn Matrix in Field k
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Primitive 5th root of unity extension
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Proof: Why a = axa When A is a Ring & Jac(A)=0
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Z_4 is not a Semisimple Z-Module of Finite Length: Explanation and Example
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Proving Artinian of Commutative Noetherian Rings with Maximal Primes
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Proving I1*I2 is an Ideal in Commutative Ring R
  • · Replies 9 ·
Replies
9
Views
12K
Undergrad Ker(phi) = {0}, then phi injective?
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad IS f(x)= x^4 + x^3 -x^2 - 2x -2 irreducable over Q?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate The converse and proving whether or not the converse holds
  • · Replies 1 ·
Replies
1
Views
5K
Undergrad What Does the Equation || (x,y,z)T ||2 Represent in 3D Graphics?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Summation involving von Mangoldt function
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad Prove (n^5 - n) is divisible by 5 by induction
  • · Replies 6 ·
Replies
6
Views
25K
High School Can Computers Generate Random Numbers?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate My definition of an artianian module is : A module is artinian if
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Proof of eAe as Division Ring when Ae is a Minimal Left Ideal
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Proof of Semisimple Modules: Finite Summands & Finite Generation
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Natural isomorphism of Left adjoints
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Can a Conjecture Be Proved Empirically?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Sum of Vector Spaces U & W in Linear Algebra Done Right
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Categorical extension of Cayley's Theorem
  • · Replies 3 ·
Replies
3
Views
3K
High School Solve Matrix without Calculator: Find Values of X
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Group Homomorphism Formula Isomorphism for Integer Sets
  • · Replies 7 ·
Replies
7
Views
4K
Graduate What is a Possible Algebraic Proof of Case 1 of Fermat's Last Theorem?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Is This Field Extension Galois?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Recursive solution of determinants
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Understanding Spivak's "Calculus on Manifolds" - Ken Cohen's Confusion
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Proving Indefiniteness of a Quadratic Form on a Subspace | V -> R
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Number Theory: Proving Statements with Verbal Arguments
  • · Replies 7 ·
Replies
7
Views
3K