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.
What U(n) or SU(n) or their multiplication isomorphic with SO(8)?
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What Is the Span of a List of Vectors in Linear Algebra?
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Does ef|g Imply e and f Are Both Factors of g?
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Prime Ideals of direct sum of Z and Z
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(x^k) - 1 = (x - 1)*(x^(k-1) + x^(k-2) + + x + 1)
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Is Every Square Integer of the Form 4n or 4n+1?
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Calculating Tilt Angle for Mounted iPad Using Accelerometer Readings
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What is the purpose of <-i> in a complex number subgroup?
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Show that linear transformation is surjective but not injective
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The General Linear Group as a basis for all nxn matrices
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Questions about the prime counting function
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Contrapositive proof of irrational relations
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How would one prove the dihedral group D_n is a group?
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Is It Reasonable to Assume a Prime Gap of at Least 10 Before Twin Primes?
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Question about Newton's method for solving a function
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Covariance matrix in barycentric coordinates
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Figuring Out Spanning w/ Vectors of 3 Components
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Efficient Prime Number Algorithm: Seeking Feedback and Offering Unique Insights
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Can Fermat's Equation Be Solved with Non-Positive Integers?
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Bicyclic Monoid: Not Concatenation?
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Do Intervals [2,3] and [2,5] in Real Numbers Share the Same Cardinality?
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Converting between bases without base 10 mid-step
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New Points of View on the Selberg Zeta Function
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Do complex number have anything like consecutive numbers?
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Directional scaling (of an ellipse)
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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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Affine spaces and time-varying vector fields
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How Do Permutations Act on Vector Spaces in S3?
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Proving (a weaker form of) Bertrand's postulate
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Dimension of Vector Space R^X: Finite/Infinite Cases
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Coordinate Space Transformations
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Cyclic set: Difference between generator and unit
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What is the purpose of introducing the transpose in this proof?
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Finding the eigenvalues of a complex matrix
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What is the basis for a vector space in Structural Engineering?
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Question on the dimension of Killing-form
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An algebraic proof of Fermat's conjecture
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Base changing for transcendental numbers
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Hermitian matrices and unitary similarity transformations
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What is the error in this proof of uniquness of row echelon form?
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Can Every Element in a Finite Cyclic Group Be a Generator?
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Deriving the Identity: (1+2+3+...+n)^2 = 1^3 + 2^3 + 3^3 +...+ n^3
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Sets closed under complex exponentiation
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Is it possible to approximate an equation with circulant and toeplitz matrices?
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Are 2^((n-2)/2) - 1 and 2^(2n) + 1 Relatively Prime?
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Why is the smallest subgroup of G containing A and B equal to G itself?
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Solving 4th Order Polynomials: Methods and Tips for Finding Roots
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Finite Dimensionality of Endomorphism Ring in Simple Modules?
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Can a group have repeating elements?
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What Is Lockwood's Identity and How Does It Relate to Pascal's Triangle?
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Finding the rank through row operation
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Understanding Simple Lie Groups: Definition and Common Misconceptions
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Are Sylow Subgroups' Products Always Subgroups?
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How Can You Find 'y' When ((m*y) mod n) ≡ (n-1)?
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When is an element of a finitely generated field extension algebraic?
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Alternating Group A_n - What Is Subgroup with Index n?
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Explaining Finite Solvable Groups: Understanding Burnside's Theorem
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Question regarding basis of function space
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Real Eigen Values: Proving/Disproving Matrix AB
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MHB Eigenvalues and Eigenvectors of a Non-Diagonalizable Matrix
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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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When is a matrix positive semi-definite?
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Finding x through mod regarding G.C.D
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How to Compute Eigenvalues Using the QR Algorithm?
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Is There an Algebraic Solution for 36=X^X?
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Non Integer Exponents for Cartesian Products
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Complexes C and C^n as Vector Spaces.
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Invertibility of Symplectic Matrices
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What is the Definition of an Ordered Field?
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What is the Riemann Hypothesis and why is it so difficult to solve?
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The nullspace of a transposed matrix
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Group Presentations - do they determine the group
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Confused about the True Geometric Meaning of a Dot Product Answer.
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Do Columns of M² Form a Basis?
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Computing the Galois Group of a Univariate Polynomial (Irreducible or reducible)
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(another)interesting number theory problem
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Maths: Prove Distributive Lattices
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A system of nonlinear equations (power sum)
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Can you switch rows in a matrix without actually switching them?
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Representations of the cyclic group of order n
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Quotients of direct sums of modules
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Basic definition of Quadratic Fields
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Asymptotic formula for the sum of log(p)/p
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Centre of the real Hamilton Quaternions H
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Isomorphism of the Dihedral group
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Isomorphism between groups of real numbers
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Bounding a prime number based equation
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Matrix Inequality: Is BTB <= B1TB1?
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What Are the Rules for Diagonal Elements in LU Decomposition?
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How Does a Vector with 3 Components Span a Plane in Linear Algebra?
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Contravariant vs Covariant components - misprint?
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Why Is the Rank of a Matrix Equal to Its Number of Pivot Points?
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Galois Groups for a system of Linear equations?
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Is There a Method to Find the Inverse of a Singular Matrix?
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What is the Post-office Problem for n>2?
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Residue field of p-adic integers
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Proof of existence of opposite roots in semisimple algebras?
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