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.
High School Core of matrix (pure translatio)
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Undergrad What does the 'X' mean in the Mueller matrix rotation equation?
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Graduate Proof, intersection and sum of vector spaces
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Graduate Apparent fallacy in linear operator theory
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Graduate Why eigenvalue specification reduces the no. of LI equations?
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Graduate Is e^ix multivalued, roots of unity, etc
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Graduate Solving AX=B with Preconditioned Conjugate Gradient Algorithm
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Graduate Isomorphism between R^inf and a proper subset of R^inf
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Graduate Can Any Inner Product Be Defined in Infinite Dimensional Vector Spaces?
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Graduate Finding Fixed Points of Affine Transformations | EWW
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Graduate When do objects factorize uniquely?
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Graduate Help w/ Proof in Category Theory
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Undergrad Diagonalizable Matrices & Eigenvalues
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Undergrad Finding Axes of Conic Section Equation
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Undergrad Does divisibility apply to imaginary numbers?
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Undergrad What is the identity for coplanar, non-collinear vectors?
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Graduate Odds that two numbers are coprime
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Undergrad What are the rank conditions for consistency of a linear algebraic system?
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High School How can I improve this equation to work in all cases?
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Undergrad Find P.Q & Q.P from Permutations of X (1,2,3,4,5)
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Graduate How Can I Derive a Set of 3x3 Matrices Analogous to the Pauli Matrices?
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Undergrad Is a Two by Two Matrix a Basis if ad - bc = ±1?
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Graduate Happy holidays,BenDecomposing tensor product of GL(2,C) representations
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Undergrad Linear Algebra transformation Question
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Graduate Do Non-Associative Groups Exist and What Are Their Applications?
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Undergrad Why 30 is the largest integer such that none of its ?
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Undergrad Relation between rank and number of non-zero eigen values.
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Undergrad Linear Transformation from R^2 to R^3
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Graduate Novel Constant \sum and \int s^{-s} - Defining a Fundamental Constant?
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Graduate Questions about group presentations
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Graduate This upper limit is wrong I need a help
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Undergrad Does group theory deal with asymmetry?
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Undergrad Understanding the Properties of Dot Product: Is it Truly Associative?
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Undergrad Finding Arbitrary nth Roots of -1 Algebraically
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Graduate What is group theory all about?
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Undergrad Matrix Multiplication and Addition with Identity and Zero Matrices
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Graduate Relating Two-Dimensional Vectors and Complex Numbers
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Undergrad Solving Equations Involving A⁻¹, B⁻¹ and C⁻¹
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Graduate Root of Non-Linear Eqn (Numerical Method)
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Graduate Zeta function in the critical strip
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Graduate What Are the Key Concepts of Dual Vector Spaces?
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Graduate Is the Inverse of a Matrix a Continuous Function?
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Undergrad Quadratic forms, diagonalization
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Undergrad Calculating Pi in Binary: How Many Decimals Do I Need?
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Graduate Raising Matrices to power of n. (complex)
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Undergrad Mappings and Inverses: More Than One Left Inverse?
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Graduate What is the definition of R in the tensor product construction?
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Undergrad Yes, that was exactly what I couldn't get. Thank you for clarifying it for me!
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Undergrad Understanding the Ordered Basis in Linear Algebra
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Undergrad Three Digit Prime Number Puzzle: Forming Primes with All Prime Digits
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Graduate What is the proof for GCD(n.m)=1 if 2^m-1 and 2^n-1 have a common divisor of 1?
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Undergrad Can a Matrix Be Expressed as a Sum of Diagonalizable and Nilpotent Matrices?
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Graduate How Accurate Are Partial Sums in Estimating e^N?
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Graduate Hermitian vs. self-adjoint operators
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Undergrad Are Column Vectors in AB Unchanged if Linearly Independent?
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Graduate Cracking the Code: Decoding the Pattern of 3D Mirror Inverted Numbers
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Graduate Su(2) Lie Algebra in SO(3): Why Choose Omega/2?
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Graduate Uniquely n-Divisible and Torsionfree Groups in Exact Sequences
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Graduate Tensor components of a Hodge dual
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Graduate Unsolvable Exponential: Solving x = y^y
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Graduate Carmichael Number: Proving $(d+p)(p-1)$ Divisor of $q-1$
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Undergrad A Challenge: Uncovering the Pattern of Prime Numbers
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Graduate Identity of Zeta function
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Undergrad Can You Solve the Equation X^2 + Y^2 + Z^2 = NXYZ for Natural N?
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Graduate Imaginary Zeros of Zeta Function
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Graduate Mobius Inversion, finite subgroup
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Undergrad Chance of random walk returning to origin
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Graduate Where Fibonacci numbers surpass prime numbers
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Graduate Symmetric group (direct product and decomposition)
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Undergrad Linear Algerba - Finding linearly independent vectors
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Undergrad Why Use the Last Row of the Elimination Matrix for Left Nullspace?
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Graduate Solving a Puzzling Problem: No A Exists for Symmetric Matrix B
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Graduate If the z-transform of x[n] is X(z)
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Undergrad Systems of algebraic equations
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Graduate Hilbert spaces: Explicit example of an unbounded operator?
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Graduate Difficult polynomial and determinant formula
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Graduate What is the Concept of Zero Double Trace in Tensor Analysis?
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Undergrad Finding Inverse of 6x6 Matrix: A Numerical Solution
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Undergrad Is (x^4)+1 Reducible over Z5 and Z?
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Graduate Why is the Gram-Schmidt Process Numerically Unstable?
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Graduate Galois extension, lattice of subfields
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Undergrad How is a matrix diagonalised?
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Graduate Isomorphism of su(2) and sl(2,C): Tensor w/ Complex Numbers
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Undergrad Is This Norm Equality Correct for \( Ax \)?
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Undergrad Finding a vector orthogonal to others
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Graduate Irreducible polynomial, cyclic group
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Graduate What Are the Subfields of F=F_{p^{18}} and Their Lattice Representation?
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Graduate Proving Vector Space Relationships in WU{A} and WU{B}
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Graduate What are the properties of valuation rings and their ideals?
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Graduate Solve a system of linear equations Ax=kb
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Graduate How Can You Define an Inner Product to Orthogonalize Arbitrary Basis Matrices?
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Graduate Z[i]-module Question: Finding Torsion and Integer r for Module M
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Graduate What is the Significance of the Orbit of P in Sylow's Theorems?
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Undergrad Understanding Ax=b: Linear Dependency & Solutions
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Undergrad Finding Basis for Matrix Transformation: SBT = E_k
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Graduate Number of primative roots in finite fields of order p^n
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Graduate Vector Product in C³: Explained & Standard Basis
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Graduate Symmetries and Transformation Groups of Equilateral Triangle & Icosahedron
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Graduate Is My Lie Algebra 4D or 5D Given These Structure Constants?
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Undergrad Plotting Pythagorean triples in a polar form
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