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.
Real Life Applications of Infinite Solutions with Gaussian Elimination
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How Many Groups Exist with Order 24?
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Galois Theory: 4 Steps to Understanding for Undergrads
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Inverse Matrix: Real-Life Applications & Uses
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Proving N is Maximal Ideal of G in Real Functions
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Generating function for groups of order n
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A Pattern I Noticed: -1 Inverts Everything?
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Vector iteration/Power method for eigen values
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General Equation for Linear n-Subspace of C^n
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Row operations performed on two matrices
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Conjugate fields and conjugate subgroups of an automorphism group
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Roots of unity form a cyclic group
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The product of 8 consecutive natural numbers will not be a perfect square?
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Roots of polynomials as nonlinear systems of equations
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Can linear algebra convert the minimum column vector in a matrix?
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To prove that a field is complex
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Determining invertibility of a matrix
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History of matrices and determinants?
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What Can Be Said About the Eigenvalues of B^{-1}A Given A and B?
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About orthogonality and nullspaces
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What makes this an Eigen value problem and why?
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MHB Finding galois group of Fq(x^(1/(q-1))) over Fq(x)
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Regarding fixed points in finite groups of isometries
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When is a Galois group not faithful
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Verification sequence of eigenvalue problem
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MHB Finding irreducible factorizations
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Understanding Least Square Solution for Random Matrices: A Comprehensive Guide
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Proving W is a Subspace of P_3 & Finding a Vector Not in W
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What is the nth term of this matrix?
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Is Eisenstein's Criterion Applicable to Polynomials in the Gaussian Integers?
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Is An a Normal Subgroup of Sn? A Proof and Explanation
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Are Scalar Quantities in Physics really 1-D Affine Spaces in disguise?
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Extended Goldbach: every odd number the sum of 5 primes
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A variation on a classic problem
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Subspace as a Direct Sum of Intersections with Basis Partition?
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Can (Z/10557Z)* be written as Cn1 x Cn2 x Cn3 with n1 dividing n2 dividing n3?
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Why is the Vector Product Operation Considered Multiplication?
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Solving the Subset Problem: Finding the Count of Valid Sets from 1 to N
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Subspace, vectorspace, nullspace, columnspace
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Solving a large under-determined system of linear equations
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Eigenvalue Question: Can I have an Infinite Matrix?
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Understanding Rank One Matrices and Their Application in Nullspace and Row Space
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How to detect redundant equation from a system of nonlinear equation?
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Miscellaneous questions on operators
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How Can You Maximize a Linear Equation with Multiple Constraints?
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Is the Goldbach Conjecture Finally Proven?
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Question about sample covariance matrix
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Is the Field of Reals in and of itself a Vector Space?
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Are all order 4 groups only isomorphic to C4 or C2+C2?
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Solution for Goldbach Conjecture
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Can You Find a Number n with Rational Square Roots for n-7, n, and n+7?
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Can there be more than one definition of a GROUP?
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Is image and range of a LT the same thing ? (Why are they named like that)
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How can you determine if a vector is perpendicular to a plane?
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The Odd Only Spiral (A twist on the ulam spiral with an interesting property)
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MHB How Do Sets W, Y, and Z Intersect?
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How can I solve equations by rearranging them?
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Relationship between eigenvalues and matrix rank
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MHB Find the Inverse of a Vector: Solve for x in Terms of b
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Linear independance and span (Definition)
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So, no prefixes...Do planes in higher dimensions satisfy Euclid's definition?
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Help me understand the inductive solution to the lines in the plane problem?
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Nonhomogeneous system of linear equations
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A question about definition of a category
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Homogeneous least squares
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Is (n+1)(2n+1) Always a Multiple of 6 for All Natural Numbers n?
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Proving one element in the symmetric group (s>=3) commutes with all element
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About vector space and subspaces
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For separable extensions, why may we argue as if they're finite?
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Transformation Matrix from x-axis
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Determine optimal vectors for least squares
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Counting Theorem: Creating Squares w/ 8 Equilateral Triangles
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Dimension of the circle in the plane is 1
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2^k+1 never divisible by u(8x-1) in integers
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Determinant of symmetric matrix with non negative integer element
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Is the Determinant of a Symmetric Matrix with Zero Diagonal Elements Non-Zero?
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Proving Adjoint of an Operator in Hilbert Space: Common Mistakes Explained
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Prime Ideals: Abstract Algebra Example
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Finding basis of a column space/row space
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Understanding the Normalization of Pauli Matrix in Quantum Mechanics
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Find if Parametric equations are perpendicular
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Some basic question about a quotient ring
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Are There Relationships Between the Column Vectors of a Matrix and Its Inverse?
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Proving the Relationship between Operators on a Finite-Dimensional Space
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Are There Ordered Fields Beyond Real Numbers and Rationals?
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Why is x^p - a irreducible over a field of characteristic p?
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Positive definitive matrix in wikipedia
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Demonstrating that (im τ) \cap (ker τ) is the Zero Space
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Can the Angle Between Two 7-Dimensional Vectors Be Calculated?
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Can a Non-Zero Tensor Product of Modules Be Zero?
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MHB Finding elements in a quotient ring
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MHB Proving Z[√(-3)] is not a euclidean domain
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MHB What Are the Units in the Ring $\mathbb{Z}[\sqrt{-7}]$?
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Multiplication of incompatible matrices
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Efficiency and the Euclidean Algorithm
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MHB Finding the units in the ring F[x]
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Inverse of Lower Triangular Matrix
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About the number of irreducible elements in UFD ring
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Dimension formulas for Lie algebras
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Maximizing Your Tips and Tricks for Focusing on Key Elements
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