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.
Cancellation Law in Group Theory: Proof and Validity
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Does SO(3) Have Nontrivial Complex 2-Dimensional Representations?
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What Does Converting a Matrix to Tridiagonal Form Indicate in Practical Terms?
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Understanding Identity Elements in Abstract Binary Operations
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A question about simple Weyl reflections
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Having trouble understanding a dimension reduction step in a matrix.
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What Is the Condition Number of This Piecewise Function?
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Is the Generated Set of a Group Closed Under Group Operation?
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Eigenvalues of a tridiagonal matrix
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Can Abstract Algebra Inspire New Tools for Ruler and Compass Constructions?
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Horner's Method vs (x-1)^n: Which is More Accurate for Evaluating Polynomials?
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Can the Empty Set Span the Zero Subspace? Insights on Spanning Sets
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Example of PID and its maximal ideal
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Can the Graham-Schmidt Process Start with Any Vector?
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Please check my solution to this invertibility test
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Decompose number in Gaussian interger field
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Is A + 2A^(-1) Invertible If A Is Invertible?
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Finding the Product of Primes: A Number Theory Puzzle
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Show that these vectors are in a vector space?
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Is This New Algorithm Effective for Finding Common Factors?
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Is a Commutative Group with a^2=1 Always a Group?
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Numbers which are not ultimately functions of integers
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A question about quadratic residues
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Laplace transform as rotation. In what space?
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Solve the Euler Totient Puzzle: Find k such that phi(k+n)=0 mod 79
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Are These Linear Algebra Statements True or False?
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Number system with an irrational base
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What Is the Difference Between a Transition Matrix and a Jacobian?
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Is \( u^p \) a root of \( f(x) \) over \( GF(p) \) if \( u \) is a root?
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Linear Algebra Preliminaries in Finite Reflection Groups
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Maximizing Distance in the Travelling Salesman Problem: Is it Possible?
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Maximizing Sum of Finite Sets: Solving Simple Arithmetic Question
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Representation Theory of Finite Groups - CH 18 Dummit and Foote
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Is Number Line Density Constant or Variable?
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Negative diagonal elements in Incomplete Cholesky Decompostion
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Logarithmic Integral and Primes
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The Orthonormality of real valued Functions
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Are any two infinite-dim. V.Spaces isomorphic?
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Product of two subgroups and intersection with p-subgroup
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Minimum number of elements to in one set to sum to all in another.
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Proof of the Order Divisibility Property
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Can Dependent Variables Defy E(X)E(Y) = E(XY) in Probability?
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MHB Number of elements in a ring with identity.
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MHB Is 1_R Equal to 0_R in a Ring? Understanding the One-Element Ring Concept
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A general condition on polynomial roots
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Order of error for rational approximation of irrationals
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A question regarding arithmetic progressions
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Infinitely many solutions ? n*phi(n)=k
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Proofs and puzzles for beginning mathematicians
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Primality Criteria for Wagstaff numbers
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MHB Proving Determinant: u,v in R^n | Det(I + uv^T) = 1 + v^Tu
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Is V a vector space? and Show that W is not a subspace
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Would someone tell me about the importance of number theory?
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Proving A = B in Linear Algebra using (A-B)D = 0 and Inverses
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MHB System of Equations: Advice Needed - Rank(A|B) Explained
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Which Book Should I Start With for Learning Number Theory?
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Number Theory Proof Help: Show p-1 & p^(e-1)|∅(n)
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MHB Proving Irreducibility of x^4 −7 Using Polynomial Theorems
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MHB Which Coefficient Ring Makes f=x^2+1 Irreducible?
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Similar to Collatz Problem (Please Read)
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Proving the Infinitude of Primes: Euler's Proof and Its Limitations
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Graphical modeling of a dynamic system Help
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MHB Ring Theory: Proving Subrings and Ring Generation
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How were these linear motion equations derived?
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Is the concept of prime numbers biased by their factorization definitions?
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MHB Which Permutations Should Be Excluded in Leibniz Formula for Determinant?
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Problem with minimizing the matrix norm
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Is i^i equal to e^-(pi/2 + 2npi)?
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Can't understand technique for computing transformation matrix
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What is the Proof of the Size of Divisors for Integers?
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Understand Affine Subsets & Mappings: Research Project for Undergrads
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Squared norms: difference or notational convenience
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MHB Proving Finite Domain Identity Element: Tips & Tricks
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How can the endless square root problem be solved?
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What is the Correct Way to Find Eigenvalues and Eigenvectors of a Matrix?
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MHB Prove Ring with Identity on Set S with One Element x
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Gram-Schmidt Method for orthogonal basis
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The approach to project out certain vector
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Symmetry Groups Algebras Commutators Conserved Quantities
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Is (a,b) the GCD of a and b in a Divisibility Proof?
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Algebra Isomorphism: Complex Numbers C over Reals R
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Determine if a matrix if positive definite
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Some Flat Equation Prime Number Aproximations
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How Do You Calculate the Dimension of F(u,v) Over F(u)?
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Nilpotent operator or not given characteristic polynomial?
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A prime limit that seems to approach a constant
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Can You Find the Prime Factors of m Using Euler's Totient Function?
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How to Add Base-Six Numbers and Express the Sum 3546 + 4326 as a Base-Six Number
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Linear or conjugate operators and automorphisms on the lattice of subspaces
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New Test for Primes form 8n =/- 3
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Consecutive Numbers in the Fibbonacci Sequence and Sums of Two Squares
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Do Quasiperfect Numbers Really Exist?
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How to factor a polynomial modulo p?
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Product of a third- and second-order tensor.
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Easy algorithms to produce big numbers
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Linear Algebra. Proving differentiable functions are a vector space.
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An error related with matrix exponential
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Qube root of 2, zero of second order polynomial
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Verifying Subring: Check Closure with ℂ & \alpha
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Fibonacci sequence- advanced realations
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