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 Linear combination of linear combinations?
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MHB Which one of these statements is wrong ?
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MHB Matrix representation of T with Basis B?
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Graduate Can You Explain the Relationship Between a Basis and Its Dual Basis?
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MHB Solving an Unsolved Math Problem: Ring A & Polynomials
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Graduate Matrix trace minimization and zeros
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MHB Indicial Notation 2: Proving $\mathbf{a}\times\mathbf{b}\cdot\mathbf{a} = 0$
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MHB For which values of k the matrix is diagonalized ?
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High School How to calculate rank of 2 by 1 matrix?
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Undergrad Solving a system of 3 nonlinear equations
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Undergrad Is the Empty Set a Vector Space?
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Graduate Abstract Algebra - Natural Numbers Proof
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Undergrad Where would I use quadratic forms and how?
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MHB Solve Autoregressive Model Problem
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Graduate Question about SO(N) group generators
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Graduate Free R-Module Basics: What is a Copy of R?
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Graduate Generalized Associative Law for Groups
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MHB Technical problem with eigenvalues
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MHB Prove that this matrix equation has no roots
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MHB Vector Proofs: Constant Magnitude and Orthogonality in Finite Dimensional Spaces
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MHB Solving Vector Manipulation Problem with $\lambda$, $\mathbf{b}$, $\mathbf{c}$
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Graduate A question about invariant factors
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Graduate Nagging Math Ques #1: 'Pseudo-Inner Product'
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MHB What Is the Structure of This Quotient Group?
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Graduate Why is this matrix bad conditioned?
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Graduate Mersenne Primes: Identifying & Eliminating Non-Prime Numbers
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Undergrad Why Does a Singular Matrix Imply Infinite or Zero Solutions?
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Graduate Multilinear Functions and Polynomials
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Undergrad Shedding some light on the dot product
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Graduate Understanding generating sets for free groups.
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Graduate Is there a relationship between odd composite numbers and their factors?
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Graduate How Do We Prove Something is a Submodule?
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Undergrad What is the difference between a vector field and vector space?
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Undergrad Inverse of a Matrix - Understanding Why We Note Relatively Prime Expressions
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Graduate An optimization problem worthy of our attention
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Undergrad Do Galois Theory Applications Influence Physics?
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MHB Unusual algebra problem (having trouble understanding the explanation)
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Graduate Can a topologically bounded set in a tvs contain a ray?
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Undergrad Is the set of prime pairs (p, p+2) finite?
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MHB Prove there exists a matrix with certain entries and determinant
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MHB Linear Dependency: Find x for a,b,c in R3
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Graduate Can Different Access Patterns Improve a Matrix's Condition Number?
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MHB Linear Dependence of Vectors Spanning a Space: Example Needed
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Graduate Number of unique ways of stacking n blocks
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Undergrad New to Linear Algebra: Confused on Reduced Row Echelon Form
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Undergrad How do I properly set up the matrix for polynomial regression?
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High School Vectors - write ordered triples in vertical or horizontal form?
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Graduate Questions about Proving R/I is not the Zero Ring
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Graduate The Spectral Theorem in Complex and Real Inner Product Space
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High School A Few Numbers With Strange Qualities
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Undergrad Some technical questions about spans and bases
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High School Understanding 3x3 Matrices: An Overview
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Graduate Rank of a matrix and max number of missing values
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Graduate Transition Matrices: Solving X[T]X & T(v_1)=v_2
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High School Why do we choose to have perpendicular axis?
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MHB Question about Linear Dependency
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High School Very basic question about vector orientation
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Graduate Complexity of a quadratic program
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MHB Linear Dependency: Proving Vector Independence in V
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Undergrad Minimum table size to contain combinations 000 to 999 in adjacent squares
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Graduate How can matrices be used as a basis for linear mappings?
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Graduate Finding the Equation of a Plane in R3 Using Intersection Points and Distances
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Undergrad What is the proof of this theorem in Vector Spaces ?
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Graduate New idea about Integer Factorization
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Graduate What Is a Pseudo-Orthogonal Matrix?
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Graduate Understanding 2-Transitivity in Multiply Transitive Groups
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Graduate Finite Difference Method, Leapfrog (2,4) CFL Condition
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Undergrad General algorithm for a magic square
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Graduate If V is a complex inner product and T is an operator on V such that <Tv,v> = 0
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Graduate Proving Diagonalizability of Adjoint Operator on Finite Inner Product Space
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MHB Automorphism of order 2 fixing just identity. Prove that G is abelian.
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MHB Proving the Inverse of the Adjoint Matrix Property for nxn Matrices
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Undergrad Can m(m+1) Equal kn for Natural Numbers m, k, and n?
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Graduate Inner Product Space of two orthogonal Vectors is 0 , Is this defined as it is ?
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Undergrad Understanding the Usefulness of Vector Projection
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Graduate Some ideas concerning the Goldbach conjecture
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Graduate Explicit solution. Properties of vector norms
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MHB Repeated eigenvalues of a symmetric matrix
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Graduate Equality of Operators A & B on Hilbert Space H
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Graduate About interesting convergence of Riemann Zeta Function
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Undergrad Why do we need to convert to a diagonal matrix?
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Graduate How can we use the Singular Value Decomposition (SVD) for image compression?
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MHB Exploring the Importance and Applications of Singular Value Decomposition (SVD)
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Graduate NxN-complex matrix, identified 2Nx2N-real matrix, determinant
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Graduate Repeated eigenvalues of a symmetric matrix
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Graduate What do we mean by 'Equivalent Projective representation ?
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Graduate Every feild has a subset isomorphic to rational numbers?
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Graduate Puzzled about characteristic polynomial output from my calc
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Graduate Is This Quadratic Form Positive Definite or Indefinite?
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Undergrad How does the change of basis theorem work in linear algebra?
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Undergrad Intuitive explanation for the general determinant formula?
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Graduate Eigenvalues of a complex symmetric matrix
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Graduate Infinite ring with exactly two non trivial maximal ideals
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Undergrad Orthogonal set - Geometric interpretation
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Graduate Can you explain me why this is also isomorphism?
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Graduate How can I write the determinant as traces in this paper on complex matrices?
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Graduate Group action and equivalence relation
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Undergrad When to use RREF in finding Eigenvectors
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Graduate If F is inner automorphism , what does this mean ?
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Graduate Are All Generating Sets in a Free Group Equally Cardinal?
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