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.
What's the difference between polynomials and polynomial functions?
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Linear least square method for singular matrices
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Can the Prime Factorization of A + B Reveal Insights About Coprime Numbers?
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Relation between Primes: Proving (2m-1, 2mn-1/2m-1) = 1
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Are the eigenvectors of A and A^T related?
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What Can be Said About the Kernel of a Tensor Product of Linear Maps?
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Invertibility of a product of invertible matrices
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Are Units in R[x] Exactly the Same as Units in R When R is an Integral Domain?
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Tensor product vector spaces over complex and real
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How to Prove a Congruence in Modulo pq with Distinct Primes?
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System of 4 quadratic equations with 4 unknowns
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Torsion-free modules over a Discrete Valuation Ring
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How to Derive the Inverse of the Sum of Two Operators?
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No real number x such that x<|0| where
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Elegant proof of fermats last theorem 2. try
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Is Every Rootless Polynomial Over a Finite Field Prime?
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Quaternions and metric of the 3-sphere
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Rearrange Formulae to Find u, v, and a
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Can the Fermat's Last Theorem be expanded to higher powers?
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Formula for the Number of Units in a Ring Modulo a Prime Power
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Distance between invertible elements of a normed algebra
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Understanding SO(1,3) and Its Applications in Mathematics and Physics
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Linear Algebra: basis and matrices
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Linear differential operator / linear transformation
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Unique Factorization: Proving for Polynomials in x
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Elegant proof of Fermats Last theorem?
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Group of rigid rotations of cube
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Can two consecutive odd primes sum to a product of three integers?
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Proving Simultaneous Diagonalizability of nxn Matrices A and B with AB = BA
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How Can a Number Be Written as a Sum of Squares or Primes?
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Isolating vector b from equation in form (axb)xa
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Why are the tensor products over Q and Z_n equal?
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Difference between a standard and metric?
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Show that all simple groups of order 60 are isomorphic to A5.
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Mathematical notation for elementwise multiplication
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What is a Regular Transition Matrix
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Algebra of Physical Space vs. Spacetime Algebra
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Proving G Abelian iff G/Z(G) is Cyclic
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Prove Rank & Similarity of Matrices A & B
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Factorization & Congruence to 4: Proven or Researched?
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Linear Transformations,Find basis of kernel and range
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Eigenvalues and eigenvectors of a matrix product
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Are Non-linear Functions Also Homomorphisms Between Modulo Groups?
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When is a group the direct sum of its normal subgroups?
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Definition of integral domain from Herstein
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Relationship among LCM, GCD, and coprimes
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How to Use the First Isomorphism Theorem to Show Z/(4Z) is Isomorphic to Z4?
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Infinite Dimensional Vector Space
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Abelian Group Order: Find Largest Possible # of Subgroups
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Proving Isomorphism of Z4 / (2Z4) to Z2
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Congruence Class Relationships in \mathbb{Q}[\sqrt{3}]
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A Tetrahedral Counterpart to Ramanujan-Nagell Trinagular Numbers?
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Looking for a proof using matrices
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What Are the Surrogate Number Congruences for Moduli Other Than Its Factors?
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Group Theory: Is A a Left Coset of G?
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Integral of Log det(1-A(x).B(x)) wrt x
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Product of Groups: Understand Max Subgroups & Taking the Product of Groups
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What Are the Possible Forms of the Kernel in Linear Transformations from R3?
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Does the Matrix xyTA Have More Than One Non-Zero Eigenvalue?
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Homomorphism Construction Using Symmetry Groups
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26 is unique between a square (5^2) and a cube (3^3)
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Simple Abelian Groups: Can They Be Classified?
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How to Determine the Order of an Element in a Factor Group?
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How can the ideal generated by ab-ba force a ring to commute?
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Can a non-symmetric matrix be positive definite?
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Solving Quadratic Field Problems with Quick Tips - PhysicsForums
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Matrix of order supose 3*3 is in span of R3
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Frequency of Greatest Integer quotients
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What is the orbit of 1 in the permutation group G?
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Fortran Code for Solving Linear System w/ Least Square Method
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Matrices with all zero eigenvalues
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What Does F Represent in Group Theory?
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Solve Equation: 3^x-2^y=1 - Positive Integer Solutions
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Properties of systems of linear equations
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How to find detA if A is 4X4 matrix
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Solutions of an equation in a PID
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Finite Subsets of N: Proving Countability
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Can S5 contain a subgroup of order 7?
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Defining Notion of Congruence for Quadratic Integers in Q[sqrt(-d)]
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Beginner's doubt regarding vector spaces.
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Proof involving surjective/onto and image/preimage of sets
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A group of finite order can be infinitely large?
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What is the relationship between a matrix and its transpose in linear algebra?
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Finite field is algebraically closed under constraint?
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Prime Factorial Proof: Existence of a Prime Between n and n!
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Showing Gal(E/Q) is Isomorphic to Z4
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Simple Rings: Commutativity and Identity
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Prove Symmetry Group of Regular Polygon Has 1 & 2 Dim Irreducible Reps
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Lie Algebra differentiable manifold
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Understanding the Abstract: Defining Groups in Abstract Algebra
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How to prove the order of x,y in this case
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Does positive-definite order imply determinant order?
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Linear Transformations: Explaining the Theorem
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Why Do Irrational Numbers Exist?
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How Does Squaring a Matrix Affect Its Determinant?
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How does exp relate a Lie group to its Lie algebra?
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Linear Algebra: A Basis for a Finite Dim VS
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Prime values of integer polynomials
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A question about factoring and factors
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Understanding UFD's with Quadratic Integer & Norm Questions
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