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 What are Some Real-Life Applications of the Cayley Hamilton Theorem?
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Undergrad How was the irrationality of pi proven?
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Graduate Solve for x, a and b in matrix equation aAx + bBx = C
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Graduate How do I isolate S in this Matrix and Vector Equation?
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Undergrad What Does One-to-One Correspondence Mean in Mathematics?
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Undergrad The Fundamental Theorem of Algebra
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MHB What is the basis for each eigenspace?
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Graduate Rotating tensors (different from vectors?)
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Undergrad Question about a matrix of vector element ratios
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MHB What does the notation $||A-B||_{2,a}$ represent in terms of matrix norms?
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Graduate Diagonalize Large Hermitian Matrices Efficiently?
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Graduate Imaginary Numbers: My Number System & Research Paper
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MHB Sylow p-Subgroups of Symmetric Group: Orders & Explanation
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Graduate Significance of difference between ring and algebra
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Graduate Direct Product of Groups: Subgroup Realization and Diagonal Subgroup
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Graduate P primary group and the correspondence theorem
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Undergrad Why P^-1AP forms a triangular matrix
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Undergrad Help understanding x,y,z equations
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Undergrad Discuss a system of equations by Gauss
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Graduate Farrel Polynomials: Is It the Same as "Feral"?
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Undergrad Why sine is used for cross product and cosine for dot product?
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Undergrad PARI/GP or comparable number theory program?
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Graduate Analytical Solution for Lower Triangular Matrix w/ Non-Zero Nth Column
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Graduate Estimating 3d transformation of two triangles
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Undergrad Is it called ring because of a clock?
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Graduate How to Convert Given Grammar to Chomsky Normal Form?
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Graduate Abelian group with order product of primes = cyclic?
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Undergrad Linear Algebra: Rotation Matrix Qθ+φ
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Graduate Solving Wilson's Theorem w/ Odd Prime & Permutation
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Undergrad Determining the Point and Angle of Rotation
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Graduate Why do morphisms in category of rings respect identity
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Undergrad What are the implications of calculating the determinant of a matrix?
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Undergrad How Can You Combine Bases from Subspaces in Linear Algebra?
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Graduate Can a group have monomorphisms in both directions and still not be isomorphic?
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Undergrad How to Deduce the Normal Vector from a Given Vector Equation?
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Graduate Is the Prüfer Group Presentation Proof for Z_{p^\infinity} Possible?
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Graduate Is the signature of this matrix zero?
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High School How Can Polynomial Remainders Reveal Patterns in Algebra?
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Undergrad Numerical method: iteratation to converge on root
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Graduate Creating a least-squares matrix of partial derivatives
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Undergrad Real Life Applications of Infinite Solutions with Gaussian Elimination
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Graduate How Many Groups Exist with Order 24?
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Graduate Galois Theory: 4 Steps to Understanding for Undergrads
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Undergrad Inverse Matrix: Real-Life Applications & Uses
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Graduate Proving N is Maximal Ideal of G in Real Functions
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Graduate Generating function for groups of order n
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Undergrad A Pattern I Noticed: -1 Inverts Everything?
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Graduate Vector iteration/Power method for eigen values
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Graduate General Equation for Linear n-Subspace of C^n
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Undergrad Row operations performed on two matrices
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Graduate Isomorphism between divisible groups
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Graduate Proof of Prüfer Group Non-Existence
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Graduate Are All Groups of Order pq Nilpotent When p and q Are Primes?
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Graduate Conjugate fields and conjugate subgroups of an automorphism group
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Undergrad Finding Direction of Vector A: M & N Intersect Perpendicularly
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Graduate Roots of unity form a cyclic group
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Graduate The product of 8 consecutive natural numbers will not be a perfect square?
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Graduate Roots of polynomials as nonlinear systems of equations
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Undergrad Can linear algebra convert the minimum column vector in a matrix?
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Graduate To prove that a field is complex
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Undergrad Determining invertibility of a matrix
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High School History of matrices and determinants?
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Graduate What Can Be Said About the Eigenvalues of B^{-1}A Given A and B?
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Undergrad About orthogonality and nullspaces
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Graduate 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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Graduate Regarding fixed points in finite groups of isometries
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High School Unit vectors and vector quantities (notation)
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Graduate When is a Galois group not faithful
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Graduate Verification sequence of eigenvalue problem
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MHB Finding irreducible factorizations
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Graduate Understanding Least Square Solution for Random Matrices: A Comprehensive Guide
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Undergrad Proving W is a Subspace of P_3 & Finding a Vector Not in W
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Undergrad What is the nth term of this matrix?
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MHB Similar Matrices: Are Eigenvalues the Same?
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Graduate Is Eisenstein's Criterion Applicable to Polynomials in the Gaussian Integers?
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Graduate Is An a Normal Subgroup of Sn? A Proof and Explanation
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Graduate Are Scalar Quantities in Physics really 1-D Affine Spaces in disguise?
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Graduate Extended Goldbach: every odd number the sum of 5 primes
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Graduate A variation on a classic problem
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Graduate Subspace as a Direct Sum of Intersections with Basis Partition?
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Graduate Can (Z/10557Z)* be written as Cn1 x Cn2 x Cn3 with n1 dividing n2 dividing n3?
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Undergrad Why is the Vector Product Operation Considered Multiplication?
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Undergrad Solving the Subset Problem: Finding the Count of Valid Sets from 1 to N
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Undergrad Subspace, vectorspace, nullspace, columnspace
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Graduate Solving a large under-determined system of linear equations
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Graduate Eigenvalue Question: Can I have an Infinite Matrix?
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Graduate Understanding Rank One Matrices and Their Application in Nullspace and Row Space
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Graduate How to detect redundant equation from a system of nonlinear equation?
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Graduate Miscellaneous questions on operators
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Undergrad How Can You Maximize a Linear Equation with Multiple Constraints?
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Graduate Is the Goldbach Conjecture Finally Proven?
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Graduate Question about sample covariance matrix
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Graduate Is the Field of Reals in and of itself a Vector Space?
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Graduate Are all order 4 groups only isomorphic to C4 or C2+C2?
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Graduate Solution for Goldbach Conjecture
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Undergrad Can You Find a Number n with Rational Square Roots for n-7, n, and n+7?
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Undergrad Simple Vector Addition Question
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Graduate Can there be more than one definition of a GROUP?
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Undergrad Is image and range of a LT the same thing ? (Why are they named like that)
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