Linear and Abstract Algebra Forum

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