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 Are Vectors Always Positive in a 1-Dimensional System?
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High School Representing vector by a number.
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Graduate Is There a Consistent Way to Divide by Zero in Extended Real Number Systems?
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Graduate Span(S1 ∩ S2) ⊆ span(S1) ∩ span(S2)
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Undergrad When are linear transformations not invariant?
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Undergrad Can You Help with These Integer Algebra Homework Questions?
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Graduate Groups and Graphs: Proving Transitive Action on Vertices
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Undergrad Linear Dependency Check: {e^x, e^{2x}}
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Graduate Inner Product of 0 vector, & Complex numbers
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Graduate Conjecture for prime pairs of difference two
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High School Unit Vector Confusion: Understanding Direction & Scalar Product Formula
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Graduate Characteristic Polynomials/Eigenvalues
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Graduate Where Can I Find Generators of R4?
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Graduate Can a Polynomial Equation Generate All Primes? A Proof for Euler's Polynomial
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Graduate Expansion for the prime counting function
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Graduate For a monoid, if uv = 1, do we know vu = 1?
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Graduate Remainder of the product of the relatively prime numbers
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Graduate Discrete hellmann-Feynman theorem ?
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High School Will a Random Number Generator Eventually Repeat Its Numbers?
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Graduate If x is a cycle of length n, x^n is the identity.
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Graduate A conjecture about sums of uniquely valued primes
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Graduate Debunking the False Proof of x^TAx=0 and A Being Antisymmetric Matrix
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Graduate Explaining How Ring of Polynomials Not Having Inverses Impacts Matrix Entries
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Graduate Possible convergence of prime series
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Graduate Average minimum tries for prime factorization
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Graduate Number of prime factors
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Graduate Prove det(A+I)=0 when Matrix A is Nilpotent
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Undergrad Can Ax = λx + b Be Solved in Euclidean Spaces?
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Undergrad Why do we use the term 'axioms' for vector spaces instead of 'definitions'?
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Undergrad Matrices and linear transformations
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Graduate Null subspace of a single vector
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High School Does a number n exist where 2^n mod 3 = 0?
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Graduate Eigenvalues and Eigenvectors of Non-Singular Matrices: A Proof and Explanation
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Undergrad Solving x5 in Terms of x Using Magma
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Undergrad Calculating Dim(ran(T) & Dim(Ker(T)
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Undergrad H Math Blog: Understanding Eigenvalues and Characteristic Polynomials
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Graduate Gradient of A*B: Adding and Subtracting Terms
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Undergrad How Do You Determine if a Linear Transformation is Injective?
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Graduate Proving Associativity of Direct Product of Two Groups
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Graduate About the idempotent R-homomorphism
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Graduate Torsion Module M with ann(M)={0} and Integral Domain R | R-Module Notations
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Undergrad What Is a Matrix Signature and How Is It Determined?
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Graduate The galois group of x^4 + 1 over Q
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Undergrad Geometric representation of composite numbers
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Undergrad How to know if the given vector is less or greater than the other vector?
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High School Find the equation in the form of ax+by+cz=d
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Graduate Proof of Congruence Transformation
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Graduate Diagonalization 2: Explaining Theorem 2.5
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Graduate Eigenvectors of first-order differential equation
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Graduate Understanding Abstract Algebra: A Geometric Approach
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Graduate Galous Group Modules Self Study: Q&A
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Graduate Plot graph of points with known inter distances
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Undergrad Finding the equation of a plane in 3-space
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Undergrad How do you solve differential equations using matrices?
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Graduate Proof and Justification for Diagonalization-Ordered Basis Theorem
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Graduate A linear operator T on a finite-dimensional vector space
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Undergrad Determine if linearly independent?
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Graduate Where Can I Find Information on the Zeta Function over Primes?
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Undergrad How Are Euclidean Algorithm and Hensel's Lemma Applied to Congruences?
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Undergrad How Are Eigenvalues Used in Real Life?
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Graduate The subtle difference between matrices and linear operators
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Graduate Density of primes between square numbers
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Undergrad What are the key definitions in Linear Algebra?
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Undergrad How were these line fitting equations derived?
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Graduate Is This Formula for Generating Primes New?
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Undergrad Does this kind of matrix product exist?
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Graduate System of nonlinear algebraic equations
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Undergrad Can Vector v Be Expressed as a Linear Combination of v1, v2, v3, and v4?
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Graduate Proof on Order of Elements in a Group
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Graduate Numerically solving the null vector
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Graduate Does Randomness in Function f(n) Impact the Riemann Hypothesis?
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Undergrad Factorizing Expressions: 216x2y2+150x2+6y2+72xy2+360x2y+48xy+40x+8y+7
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Undergrad How can we fairly distribute points in a peer evaluation with 6 classmates?
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Graduate Simple category theory isomorphism
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Undergrad Poisson distribution and binomial distribution questions
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Graduate Rank of a Matrix - Physics Forum | Jennifer
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Graduate Testing a Lanczos (tridiagonalization) algorithm
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Graduate How Can Vector Identities Be Proved Using Index Notation?
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Graduate I need a second opinion on a Graph Theory proof.
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Graduate Why are the casimirs independent of the representation
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Graduate Let A be an n x n matrix such that A^3 = On
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Graduate Is There a Function f: Z -> Z Such That f(f(n))=-n for Every Integer?
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Graduate Linear independence of eigenvectors
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Undergrad Checking Graph Colorability: How Many Colors are Needed?
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Graduate What is the meaning of this expression ?
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Undergrad Learning Algebra: Questions and Advice
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Graduate Applications of Abstract Algebra?
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Graduate Embed Symmetric Group in Alternating Group A(n+2)
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Undergrad Can Music Notes Be Transformed into Mathematical Algorithms?
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Graduate Unknown primes less than largest known prime?
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Graduate Constructible root from cubic polynomial
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Graduate Is Gamma Irrational? Investigating the Irrationality of Pi and e
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Undergrad Solving an example, vectors as rows or columns of a matrix = same solution.
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Graduate Definition of the determinant i = 1
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High School Changing the subject of a formula
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Graduate Counting partitions with two givens
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High School Less notorious, but still important numbers
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Graduate Determinant of nxn Matrix as Linear Function of Each Row
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Graduate Characteristic Polynomials and Minimal polynomials
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Undergrad Understanding Phi Function and Multiplicativity
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