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 Contrapositive proof of irrational relations
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Undergrad Understand Summation Notation & Clear Confusion
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Graduate How would one prove the dihedral group D_n is a group?
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Graduate Is It Reasonable to Assume a Prime Gap of at Least 10 Before Twin Primes?
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Undergrad Are these two vectors coprime?
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Undergrad Question about Newton's method for solving a function
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Graduate Covariance matrix in barycentric coordinates
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Undergrad Figuring Out Spanning w/ Vectors of 3 Components
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Graduate Efficient Prime Number Algorithm: Seeking Feedback and Offering Unique Insights
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Graduate Can Fermat's Equation Be Solved with Non-Positive Integers?
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Graduate Bicyclic Monoid: Not Concatenation?
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Undergrad Do Intervals [2,3] and [2,5] in Real Numbers Share the Same Cardinality?
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High School Converting between bases without base 10 mid-step
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Graduate New Points of View on the Selberg Zeta Function
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High School Do complex number have anything like consecutive numbers?
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Graduate Understanding the Relationship between Group Theory and Physics
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Graduate Directional scaling (of an ellipse)
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Graduate Is There a Simple Proof of the Nullity - Rank Theorem?
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MHB Can a Matrix Satisfy \(A^2 = A\) and be Non-Singular?
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Graduate Affine spaces and time-varying vector fields
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Graduate How Do Permutations Act on Vector Spaces in S3?
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Graduate Proving (a weaker form of) Bertrand's postulate
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Graduate Dimension of Vector Space R^X: Finite/Infinite Cases
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Undergrad Coordinate Space Transformations
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Undergrad What is the Conceptual Difference Between a Matrix and a Tensor?
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Graduate Cyclic set: Difference between generator and unit
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Undergrad What is the purpose of introducing the transpose in this proof?
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Graduate Finding the eigenvalues of a complex matrix
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Undergrad What is the basis for a vector space in Structural Engineering?
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Graduate Question on the dimension of Killing-form
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Graduate An algebraic proof of Fermat's conjecture
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Graduate Base changing for transcendental numbers
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Graduate Hermitian matrices and unitary similarity transformations
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Undergrad What is the error in this proof of uniquness of row echelon form?
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Graduate Can Every Element in a Finite Cyclic Group Be a Generator?
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Undergrad Deriving the Identity: (1+2+3+...+n)^2 = 1^3 + 2^3 + 3^3 +...+ n^3
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Graduate Sets closed under complex exponentiation
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Graduate Is it possible to approximate an equation with circulant and toeplitz matrices?
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Graduate Are 2^((n-2)/2) - 1 and 2^(2n) + 1 Relatively Prime?
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Graduate Why is the smallest subgroup of G containing A and B equal to G itself?
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Undergrad Solving 4th Order Polynomials: Methods and Tips for Finding Roots
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Graduate Finite Dimensionality of Endomorphism Ring in Simple Modules?
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Undergrad Can a group have repeating elements?
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Undergrad Vectors Perpendicular to Plane: nhat
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Graduate What Is Lockwood's Identity and How Does It Relate to Pascal's Triangle?
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Undergrad Finding the rank through row operation
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Graduate Understanding Simple Lie Groups: Definition and Common Misconceptions
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Graduate Are Sylow Subgroups' Products Always Subgroups?
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Undergrad How Can You Find 'y' When ((m*y) mod n) ≡ (n-1)?
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Graduate When is an element of a finitely generated field extension algebraic?
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Graduate Alternating Group A_n - What Is Subgroup with Index n?
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Graduate Explaining Finite Solvable Groups: Understanding Burnside's Theorem
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Graduate Question regarding basis of function space
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Graduate Real Eigen Values: Proving/Disproving Matrix AB
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MHB Eigenvalues and Eigenvectors of a Non-Diagonalizable Matrix
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Undergrad Rearranging a matrix to get the minimum diagonal
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Undergrad Vector addition; spherical coordinates
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MHB A and B are two symmetric matrices
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MHB What Values of k Make These Vectors Linearly Dependent?
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MHB Is the Square Matrix A Invertible Given A^2 + A + I = 0?
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Undergrad Vectors A,B,C: Is Parallel Necessary?
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Graduate When is a matrix positive semi-definite?
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Undergrad Finding x through mod regarding G.C.D
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Graduate How to Compute Eigenvalues Using the QR Algorithm?
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Undergrad Is There an Algebraic Solution for 36=X^X?
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Graduate Non Integer Exponents for Cartesian Products
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Graduate Complexes C and C^n as Vector Spaces.
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Graduate Invertibility of Symplectic Matrices
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Graduate What is the Definition of an Ordered Field?
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Graduate What is the Riemann Hypothesis and why is it so difficult to solve?
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Graduate The nullspace of a transposed matrix
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Graduate Group Presentations - do they determine the group
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Undergrad Confused about the True Geometric Meaning of a Dot Product Answer.
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Undergrad Do Columns of M² Form a Basis?
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Graduate Computing the Galois Group of a Univariate Polynomial (Irreducible or reducible)
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Graduate (another)interesting number theory problem
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Graduate Maths: Prove Distributive Lattices
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Graduate A system of nonlinear equations (power sum)
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Undergrad Can you switch rows in a matrix without actually switching them?
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Graduate Representations of the cyclic group of order n
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Graduate Quotients of direct sums of modules
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Undergrad Help with simple matrix algebra
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Graduate Basic definition of Quadratic Fields
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Graduate Asymptotic formula for the sum of log(p)/p
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Graduate Centre of the real Hamilton Quaternions H
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Graduate Isomorphism of the Dihedral group
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Graduate Isomorphism between groups of real numbers
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Graduate Bounding a prime number based equation
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Graduate Matrix Inequality: Is BTB <= B1TB1?
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Undergrad What Are the Rules for Diagonal Elements in LU Decomposition?
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Undergrad How Does a Vector with 3 Components Span a Plane in Linear Algebra?
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Graduate General truth about elements of a matrix to the n-th power?
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Graduate Contravariant vs Covariant components - misprint?
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Undergrad Why Is the Rank of a Matrix Equal to Its Number of Pivot Points?
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Graduate What does this notation mean? Linear map A = [A^\mu \nu]_\mu \nu
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Graduate Galois Groups for a system of Linear equations?
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Undergrad Is There a Method to Find the Inverse of a Singular Matrix?
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Graduate What is the Post-office Problem for n>2?
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Graduate Residue field of p-adic integers
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Graduate Proof of existence of opposite roots in semisimple algebras?
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