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 Vector space or inner product space - ambiguous
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Undergrad Simple factorial and matrix question
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Graduate Permutation describing action on G-set
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Undergrad Cartesian equation of plane using two lines?
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Undergrad What is the significance of the zero vector in a vector space?
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Undergrad How Do You Determine the Maximum Order of an Element Modulo n?
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Graduate Dimension of a Set of Transformations
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MHB Find Center of Groups of Order 8
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Graduate Abelian group on the natural numbers (including 0) ?
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High School Does the following point lie on plane?
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Undergrad Finding out a equation of a plane that is parallel to a plane
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Graduate Is There a General Way to Format a Counterexample for Diagonal Matrices?
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Graduate Sylvester's Criterion for Infinite-dimensional Matrices
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Undergrad Linear Transformations and Bases
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4
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MHB How Many 3x3 Non-Singular Matrices Exist with Four 1s and Five 0s?
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Graduate Confusion: computation of class number of K=Q(sqrt(30))
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Graduate Understanding the Ideal Class Group of Q(√-17)
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Undergrad How to interpret absolute value bars?
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Graduate Galois Groups of Extensions by Roots of Unity
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Graduate Combinatorial Number Theory Problem
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Undergrad Confused with working out the span of a set of vectors in R^2
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2
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Graduate How to know if an infinite system of linear equations has a solution
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MHB What is the Complete Set of 2x2 Matrices Satisfying $A^2-4A+3I=0$?
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8
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Graduate Rational numbers that form a group under addition
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Undergrad Finding a basis for the following vectors.
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Graduate Equal Distances Between N Points in R^n-1+ | Solving System of Equations
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Undergrad PA=LU decomposition (w/ Partial Pivoting)
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High School Algebraic multiplicity of matrix
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Graduate How to make matrix positive definite (when it is not)?
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3
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Graduate Is the Number of Free Variables Constant in Echelon Form Systems?
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Undergrad What are Ideals and Polynomial Rings? A Simple Explanation and Concrete Example
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Graduate Help Develop Tongue in Cheek Abstract Algebra Proof
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Graduate Maximum inner product between two orthgonal vectors (in standard dot procut))
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Undergrad Show that two polynomials cannot span P2.
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Undergrad Group representations, interesting aspects?
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Undergrad Finding the basis for a set of vectors.
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Undergrad Writing a matrix as sum of a constant * matrix
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Graduate Solving Quadratic Diophantine Equations with A=0, C=0
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Undergrad Linear independence of sin (x), cos (x) and 1, proof
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High School Zeroes at the end of a FACTORIAL
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Graduate Finite Reflection Groups in Two Dimensions - R2
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Graduate So is chike obo proof of fermat's last theorem
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Undergrad Proving 2-Norm of A: Understanding the Relationship Between u and v
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Graduate Field extension, properties,proof
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Graduate Continuous matrix = differential operator?
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Graduate Are e and π Transcendental Numbers? Investigating the Rationality of e + π
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Undergrad How to calculate powers of a 2x2 matrix WITHOUT eigenvectors ?
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Graduate Proving Jordan Canonical Form for Similarity of Matrices with Same Polynomials
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Undergrad Computing a kronecker product of two matrices
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Graduate Finding Real Solutions for x-tanh ax = 0 with a>1
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Graduate Does d dividing n imply phi(d) divides phi(n)?
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Undergrad Question on subspaces and spans of vector spaces
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Graduate Offset between non-homogeneous and homogeneous recurrence sequences
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Graduate Aligning a matrix with its eigen vectors and other questions?
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Graduate Jordan Normal Form & Generalized Eigenvectors
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Graduate Induction Method: My Question About Theorem in Finite Groups
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Graduate How to learn to like number theory
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Undergrad Eigenvalues of the product of two matrices
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High School Understanding Vector Products - Mike's Query
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Graduate Mertens function : new formulation
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Graduate Help me understand a line in an ATA is positive, semi-definite proof
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Undergrad Matrix Multiplication to translate object with given vertices
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Graduate Proving that the parity of a permutation is well defined.
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Graduate Factorize x^2 - z*y^2 with Gcd(x,y)=1, Gcd(x,z)=1, Gcd(y,z)=1, and z squarefree
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Undergrad Eigenvalues & Eigenvectors: Repeated vs Distinct
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Graduate Expressing matrices as outer product of two vectors
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Graduate Putting a matrix into Rational Canonical Form
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Undergrad Matrix Multiplication and Commuting
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Graduate Describing Matrix/Transformation by Eigens.
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Undergrad How to calculate complex dot products
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Undergrad Relationship between eigenspace and column space
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Undergrad Quick question about groups and their properties
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Undergrad Algebraic multiplicity of the matrix
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Graduate Confusion between orthogonal sum and orthogonal direct sum
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Undergrad Relationship between column space of a matrix and rref of matrix
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Graduate Lanczos Method: Calculating Smallest Eigenvalues
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Graduate Can a nonabelian group of order p^3 be constructed for any prime p?
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Undergrad Mathematica Vector Fields Explaination.
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Graduate Various Proofs Regarding Divisors and Properties of Divisors
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Undergrad Definition questions for linear algebra
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Graduate Linear Algebra Proof of Span and orthogonal vector space
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MHB Are Units and Principal Ideals Related in Rings?
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Graduate Maximal number of bases for which composite number is Fermat pseudoprime
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Undergrad Solving Vector Norm with F Matrix: Advice from Jo
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Undergrad Meaning of eigenvectors and values of a 2x2 matrix (2nd order tensor)
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Graduate How Can the Fibonacci Sequence Be Proved by Induction?
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Graduate Can Eigenvalues of Matrix Addition Be Simplified?
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Undergrad What Does \Re2 \rightarrow \Re2 Mean in Linear Transformations?
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Graduate Is f(a) Always 1 or Legendre Symbol?
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MHB Solving for Unit Vectors in U Given Vector 1 and Matrix S
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Graduate How to prove that pZ is a maximal ideal for the ring of integers?
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Graduate Picard-Vessiot Extension over a Differential Field?
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MHB Proving Orthogonal Polynomials: A Weighted Integral
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Graduate Where does p = 5 (mod 8) solve x^2 = a?
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Graduate A≡b mod n true in ring of algebraic integers => true in ring of integers
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Undergrad Are these two linear maps equivalent?
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Graduate Is the Degree of Q(a) Over Q Correctly Understood?
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Undergrad How do you solve equations with matrices?
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Undergrad Diagonalization and similar matrices
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Graduate What Maps Belong to Aut(S2)/SO(3)?
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