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 Proving LCM Formula and GCD for Non-Integers
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Graduate Column Space of A'*A: Subset of A'?
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Graduate Matrix form - completing the square
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Undergrad How Can Analogies Simplify Group, Ring, and Field Concepts?
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Graduate Dot/bilinear product in C^n / Orthogonality
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Graduate Understanding Transvections:T_W:V->V Tv=v+w
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Undergrad When Does a Square Matrix Ensure Unique Solutions?
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Undergrad Can C= (pi)d Be Solved with Any Prime Values?
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Graduate Confused about definition of algebraic closure
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Graduate Is this correct? Field extension of the rationals
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Undergrad What was the motivation to define what a vector space is?
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Graduate Eigenvalues of a symmetric operator
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Graduate Same symbol, different meanings? Subgroup index & field extension
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Graduate Is the determinant a linear operation?
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Graduate Counting Cycles in S_5: Examining Conjugacy Classes and Lengths
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Undergrad Nullity of Matrix A: Implications & Null Space Span
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Graduate Testing optimality via complementary slackness
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Graduate Brocard's Problem: No Solution for n! Containing Prime^2, n>7?
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Graduate Find the sum in this given question very interesting and analytical
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Graduate Finitely generated modules as free modules
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Graduate Transforming association matrix to a functional matrix
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Graduate How to Prove Aut(H ⊕ K) ≅ Aut(H) ⊕ Aut(K)?
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Graduate Understanding Square Residue: Solving the Mystery of -1 = x^2 mod p
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Undergrad Is W a Subspace of R^3 and What is Its Geometry?
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Undergrad Determining whether sets of matrices in a vectorspace are linearly independent?
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Graduate Webpage title: How to Solve a 3D Matrix Equation
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Graduate Word for one-to-one correspondence between ideals and modules of an algebra
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Undergrad Why Is the Transpose of a Matrix Important in Linear Algebra?
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Graduate Group representations on tensor basis.
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Undergrad Theorem of mutations in a numeral sequence
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Graduate Request for introductory book on graph theory
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Graduate Need help starting a proof about an infinite square grid.
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Undergrad [Linear Algebra]- Simultaneous equation. Deriving the general solution.
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Graduate Find subgroups of finitely generated abelian groups
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Graduate Does the Picard Group Vanish for Semilocal Rings?
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Graduate Two Prime Fields Isomorphic to Zp and Zq
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Graduate Why Does H ∩ K = {e} Imply G Has Only One Element of Order 3?
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Graduate Convex set for similarity constraint
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Graduate Formulation of a linear programming model
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Graduate Calculating angles between matrices
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Graduate Sum of squares of prime factors
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Graduate Derived Subgroup (In particular Q8)
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Undergrad Formula for multiplication of trinomials
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Graduate Linear Transformation to Block-wise Stack Matrix
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Undergrad How to solve for matrix V ? A = V*S*V'
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Undergrad Simple Hyperplane Equation - What am I Missing?
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Graduate About Vector fields and vector valued functions
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Graduate How can the Cauchy-Schwarz inequality be applied to L^2 functions in a book?
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Graduate Does the Chain Rule Apply to Derivatives of Inner Products?
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Graduate Convolution and a specific function
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Undergrad Solve Linear Algebra Matrix Equation
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Graduate Explicit construction of SO(n)
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Graduate Paradox for the existence of 4,5 and 7 using Brocard's problem
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Undergrad Help with an investment matrix word problem
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Graduate Physical meaning of Eigenvalues/vectors/functions
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Undergrad Please help: determining infinitely many solutions in a matrix
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Undergrad Help Understanding Dot Product
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Graduate Rank of Matrix A with Kronecker Symbol and Sum Condition
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Graduate What Engaging Real-Life Applications Can Make Abstract Vector Spaces Exciting?
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Undergrad Proof of FLT Using High School Algebra & Number Theory
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Graduate What is the Visual Prime Pattern Based on Trig and Harmonics?
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High School Where Did the Binomial Theorem Originate?
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Undergrad Complex Numbers in Linear Algebra
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Graduate Effect on eigenvalues of multiplying by a diagonal matrix
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Graduate Understanding Adjoint Operators in Vector & Function Spaces
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Graduate Odd Prime Triples: Find & Explore Solutions!
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Graduate New Sieving Method, Goldbach's Conjecture
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Undergrad Divisibility question; consecutive numbers
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Undergrad Checking weather any positive number is zero or not
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High School Why do we need to normalize vectors for?Is it just to cut down on
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Graduate Structure theorem for abelian groups
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Undergrad How Do You Construct a Matrix to Select Specific Elements from Another Matrix?
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Undergrad Oriented angle between vectors
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Graduate Are the number of operations countable or uncountable?
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Undergrad Mapping points inside one 2D rectangle into another smaller one
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Undergrad Find values for k in a system of equations
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Graduate Infinitesimal volume element in different coordinate system
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Graduate Change of coordinates for functions
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Graduate Therefore, (mn)! is divisible by m!(n!)^m.
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Graduate Computation of Continued Fractions of irrational numbers
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Graduate Why an odd perfect number, if exists, is not divisble by 3?
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Undergrad Linear maps between finite dimensional spaces
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Graduate Find a solution for a Pell's equation
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Graduate Complementation=orthocomplementation? (Distributive lattices)
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Graduate What's the motivation for coset and quotient structure?
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Graduate Diagonalization of symmetric bilinear function
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Graduate Rearranging redshift formula for v
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Graduate Extending automorphism groups to inner automorphism groups.
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Graduate Matrix Factorization: Spherical & Cartesian Vectors
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Graduate Question in Proof of second order condition with linear constraints
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Undergrad Sum of first n Fibonacci numbers with respect to n?
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Graduate What Is the Arithmetic Gamma Function \(\gamma_{m}(n)\)?
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Graduate Are Order 1 Alternating Tensors Different from Normal Tensors?
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Graduate Conjecture: Sophie Germain Triangles & x | 2y^2 + 2y - 3 = z^2
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Graduate Pictures of abstractions behind mathematical equations?
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Undergrad Linear equations for calculating position for the GPS
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Graduate Easy question on the Second Sylow Theorem
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Graduate Representing a function in a different space
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Undergrad What is the significance of rings in understanding Fermat's Last Theorem?
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Graduate Is Rank(A) Equal to Trace(AA*) and When Does AB-BA=I Hold?
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