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.
Undergrad Explore Irrational Numbers: Find Out How Close You Can Get!
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Graduate How to Find a Maximal Subset of X in V=C[0,1]?
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Graduate How can I calculate the Killing form of a Lie algebra using a specific basis?
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Graduate Is the Adjugate of a Singular Matrix Also Singular?
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High School The Importance of Zero: Uncovering its Significance
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Graduate Vector Space P_4: Basis with Tchebychev Polynomials
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Graduate SL(2,C) & sl(2,C): Physics Book Reference
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Graduate A VERY interesting Fermat-like sequence: A_n=4^3^n+2^3^n+1
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Undergrad Triangle Inequality: True or False?
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High School Can You Solve the Equation 5^n = 80n for n?
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Graduate Find Matrix of Reflection at y=-4x & Rotation 45 Degrees Axis [1,2,2]
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Graduate Help about properties of Pell numbers
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Graduate Proving V+J=k[x] using induction for k with polynomial ring in n variables
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Graduate Ordenation of the complex number and its consequences
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Graduate Proving Independent Functions: Wronskian for n=2
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Undergrad Which Math Course to Choose for a Physics Major: Algebra I or Linear Algebra I?
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Graduate Can the Direct Sum of Cyclic Groups Determine the Properties of Finite Groups?
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Graduate Proofs in Linear Algebra: Countable Sets, Algebraic Numbers, and Fields
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Undergrad Cross Product in R^n: Defined or Undefined?
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Undergrad Curves intersecting at the origin
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Undergrad Motivations for eigenvalues/vectors
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Undergrad Infinitely Many Solutions? A Homework Problem to Investigate
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Graduate Triangular numbers, T(An +B), that equal (Cn+D)*(En+F) for all n
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Graduate Nabla operator to geometric product
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High School Applications of Linear Equations Monetary Word Problem
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Undergrad How can I prove the invertibility of a diagonalizable matrix?
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Graduate Question about zero element in vector spaces
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Graduate The Mystery of Pell and NSW Numbers: Can You Solve It?
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Undergrad Solving Line Space Problem with Matrices A & B
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Graduate I name this number the Near Integer Ratio Rv
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Graduate Discussing the Near Step Function for γ=0.4823241136337762
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Graduate Proving Similar Matrices Have the Same Characteristic Polynomial
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Undergrad Finding k for Linear Dependence in a Vector Space
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Graduate Are Orthogonal Matrices Compact?
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Graduate Confused about C Embedding in Funct(Cop, Set)
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High School Where Can I Find Resources for Learning About Matrices and Solving Methods?
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Undergrad Matrix Multiplication: Can You Multiply a Matrix in the Middle?
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Undergrad Nullspace of non-zero 4x4 matrix
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Undergrad Are These Sets Vector Spaces?
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Graduate Existence of n T-invariant Subspaces in Vector Spaces and Linear Operators
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Graduate 2 non-zero matrix A and B, and A*B=0
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Undergrad Linear (in)dependent vector sets
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Undergrad Why Are Diagonalized Matrix Columns the Eigenvectors?
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Undergrad Orthogonal Basis: Correct to Assume No Non-Orthogonal?
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Undergrad How Can We Determine the Value of p to Make Three Vectors Coplanar?
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Undergrad Anyone knows about Markov Chains?
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Graduate Me, myself and conjugate permutations
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Undergrad Expressing Natural Numbers as Sum of Primes
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Graduate Prove that a set is a monoid, but not a ring.
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Undergrad Algebra: Expressibility of f(x) with 10 Numbers
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High School How can you rearrange a formula to make a specific number the subject?
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Graduate Determinat of a continous matrix?
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Graduate Linear transformation, show surjection and ker=0.
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Graduate Visualizing the Associative & Distributive Properties of Rings
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Undergrad Patterns of Solution Sets of a System of Linear Equations
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Graduate General Definition of Relatively prime
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Undergrad Exploring Orthogonality in Linear Algebra: A Simple Proof of a Common Identity
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Graduate Operator change of basis (QM / QI)
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Graduate Understanding the Limit of Recursive Sequence R_n for x = k^2 - k + 1
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Graduate Intersection of cyclic subgroups
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Graduate Find all the homomorphisms from Z12 to Z6?
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Graduate Prove/Disprove: F1 and F2 Isomorphic as Fields
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Graduate Proof: S_n is Not Abelian for n >= 3
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Graduate Can Polynomial Maps and Ideals Demonstrate a Ring Isomorphism in Finite Fields?
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Undergrad Troubleshooting a System of Linear Equations
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Graduate Writing Natural Numbers: A Unique Expression Using Powers of 2 and Odd Numbers
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Graduate Can Any Unitary Matrix Be Expressed as e^A?
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Graduate Finite groups and order of their elements
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Graduate How Natural Isomorphisms Work: Understanding the Basics
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Undergrad What are the properties and connections between bit strings and graph theory?
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Graduate Origin of Numbers: Pythagorean Theory
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Graduate Prove Endomorphism Ring of Simple Module is a Field
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High School Mystery of 2.3: Is it Even or Odd?
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Graduate Generate All Permutations of Sn from An and 1 Odd Permutation
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Undergrad Are Skew-Symmetric Matrices a Subspace of Mat2x2(ℝ)?
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Graduate Proving Module Homomorphisms: A x B to M & M to A x B
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Undergrad Can Infinity Divided by Zero Yield One?
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Graduate What Are Right Ideals in M(n,n) and How to Explore Them?
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Graduate Proving Equality of Fields with Distinct Primes in Z
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Graduate Is the Kernel of a Field Homomorphism Trivial or Isomorphic to the Field?
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Undergrad Understanding Multiplicity and Dimension in Eigenvectors
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High School An easy question about cartesian product
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Graduate Homework question regarding irreducible representations
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Undergrad Solutions to x^2==22(mod103) in Z103
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Undergrad Solving f(x)=3x^2+7x=5 for m=23 and m=25 using Completing the Square
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Graduate Prove that inv(G) is a group. G is a monoid
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Graduate Proving K/F is Separable Extension
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Graduate Is T(inv)(0) a Subspace of V and T(V) a Subspace of W?
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Graduate Proving Isomorphism: Aut n(K) and Symmetric Group Sq^n
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Undergrad Proving Congruence: (p-1, k) ≡ (-1)^k (mod p)
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Undergrad Solution Sets and Linear Equations
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Graduate O(ab) when o(a) and o(b) are relatively prime
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Graduate Eigenvalues of the square of an operator
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Graduate Factoring x^5+x+1 Using Modulo - A Guide
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Graduate Proving Separability of E(k)/E When k is Separable Over E
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Graduate Eigenspace and lin dependency proof
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Graduate A.B= m1, B.A=m2, m1 and m2 diagonal matrices
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Undergrad How do I find the eigenvectors for this matrix?
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Undergrad Understanding Eigenvectors: Solving for Eigenvectors of a 2x2 Matrix
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Graduate Is {1/n^x} an Element of l^p for Various Values of x and p?
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