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 Putting an equation in quadratic form
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Graduate Finite Subset Max in Set S: Proof
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Graduate Some help with a number theory problem
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Undergrad Geometric Constructible Numbers
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Undergrad A Determinant's relation to permutations
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Graduate N^3 mod t covers all remainders?
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Undergrad Vector product VS dot product in matrix
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Graduate Proving Properties of an Ordered Ring: R+ & R
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Undergrad Solving a system of linear equations with computer
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Graduate Determinant of a non-square matrix?
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Graduate Prove Symmetric Matrixes Thm: A=0 or Skew Symmetric
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Undergrad Linear independence of orthogonal and orthonormal sets?
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Undergrad What Are the Mysteries of Boolean Algebra Beyond Binary Values?
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Graduate Eigenvalues and eigenvectors of a 3x3 matrix (principal stresses)[programming]
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Undergrad How to express vector in sigma notation
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Graduate Finiteness of a non-commutative ring
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Undergrad Gcd(a,b,c)lcm(a,b,c)=abc => a,b,c relatively prime in pairs
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Undergrad Basis for the indicated subspace
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Undergrad Can Matrix Addition Allow for Cancellation?
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Graduate Finding All u in R for Field Extension Q(√2,³ √5) and Proving Equality
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Undergrad How Can We Understand Division by Zero Through Logical Reasoning?
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Graduate What is the Quotient Group S/S1?
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Graduate Diagonal Linear Operator T in L(H): Examples
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Undergrad Why is the dimension of the vector space , 0?
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Graduate Solving Congruences: Proving a=b
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Graduate Why Don't All Inner Products Define the Same Vector Norm?
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Graduate What is the relationship between range and nullspace for projections?
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Graduate Is a Linear Map Always Diagonalizable in This Context?
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Undergrad Having difficulty understanding what the Range of a linear transformation is.
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Graduate How do I find all cosets in GL(n) for the set H={A in GL(n) | det(A) = 1}?
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Graduate Is REQ a maximal left ideal with invertible matrix Q?
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High School Understanding Null Space: A Layman's Explanation
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Undergrad Tensor Algebra Examples for Mechanical Engineers: A Resource Guide
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Undergrad Mathematical notation to multiply matrix elements
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Undergrad Why Multiples of Three are Divisible by 3
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Graduate How Can a Symmetric Matrix Have 2 Eigenvectors with Only 1 Eigenvalue?
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Graduate Dihedral group D5 - Symmetry of a Pentagon - Conjugacy classes
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Graduate Can induction be extended to the rationals?
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Graduate What is the Proof for the Jacobi Symbol Property (ii)?
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Undergrad How to prove that if x^n*y=y*x^n, then x and y commute
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Graduate Are proofs of impossibility always flawed and limited?
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Graduate Is There a New Formula for Prime Numbers?
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Graduate How does Cantor's concept of infinity differ from the extended real numbers?
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Undergrad Euler's Thirty-six officers problem?
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Undergrad If a 3 x 4 matrix can have independent columns?
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Graduate Which algebra vectors satisfy this (Trying to derive Schrödinger)
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Undergrad Is this matrix diagonalizable?
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Graduate Are there any primes of the form 10^k + 1 above 101?
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Undergrad Solution to time offset vector equation?
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Graduate Calculating Volume of a Parallelepiped in R^n
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Graduate Mapping Elements in Quotient Group G/N to Isomorphism f:G/N--H
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Graduate Sequence of definite positive matrices
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Undergrad Converting a Vector Equation of a Plane to a Scalar Equation
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Graduate How Can You Measure the Distance Between Two Subspaces in Higher Dimensions?
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Undergrad How Do Subspaces and Orthogonality Relate in Linear Algebra?
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Undergrad Prove that if A is upper triangular and B is the matrix
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Undergrad Polynomials in Zn[x]: Degree & n^2
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Undergrad Method for rotating data points in 3 dimensions
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Graduate Prove Wilson's theorem by Lagrange's theorem
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Undergrad How to solve two equations involving complex variables?
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Graduate Reversing Logarithmic Integral Function
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Undergrad Find Remainder with Fermat's Theorem
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Graduate Can Real Matrices Be Transformed into Complex Matrices Through Similarity?
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Graduate Is C Diagonalizable Given Its Eigenvalue Multiplicity?
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Undergrad Solving Equation from "Belt Problem": Find Alpha
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Undergrad What is the point in calculating orthonormal bases for R3
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Graduate What are some recommended resources for self-studying random matrix theory?
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Graduate Most challenging problem from I. N. Herstein's Algebra Book
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Undergrad If n*n matrix, can row space ever be equal to null space?
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Graduate Is a Zero Principal Minor in PSD Matrices Indicative of Smaller Zero Minors?
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Graduate Proving Inequalities to Induction and Simplification
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Graduate How Can f and g Be Expressed Using Elementary Symmetric Polynomials?
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High School Is there an equation to find roots?
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Graduate Expansion of Fermat's Little Theorem
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Undergrad The Equation of a Line in 3-Space
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Graduate A question on PSD (positive semidefinite) completion
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Undergrad Direct Sum/Product of Groups Clarification?
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Undergrad What is the inverse function of f(x) = c/x^(1/n)?
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Undergrad Operator Equations: Add, Subtract, Multiply & Divide
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Graduate Can Leading Principle Minors Determine Zero Elements in PSD Matrices?
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Graduate Another necessary condition for Positive Semidefiniteness?
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Graduate Convert Numbers to Rational Bases: An Example
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Undergrad Finding the base of numbers from a given equation
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Graduate Proving the Properties of Subspace U⊥ in Rn | Help with Subspace Concepts
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Graduate Commutative and Associative Addition in Closed Sets: A Conceptual Explanation
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Graduate Number theory: Binary Quadratic Forms
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Graduate Can Commuting Operators in a Hilbert Space Share a Common Set of Eigenvectors?
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Graduate Question on the set of zero-divisors of a ring
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Graduate Proving Sum-Free Sets: A Presentation
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High School Why does the 'Number 9 Phenomenon' always work in integer systems?
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Undergrad Is there a test for binary numbers divisible by 2^n - 1?
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Graduate Matrix Derivative: Solving for \partial_{x}[\det(\textbf{1}-\textbf{M})]
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Graduate Primitive Pyth. triples: Solutions of x^2 + y^2 = 2 z^2
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Graduate Understanding Growth Order of Functions in Integral Equations
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Undergrad How Do We Calculate the Determinant of a Complex Matrix?
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Graduate What is the Basis for an Extension Field Adjoined with an Element?
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Graduate Order of Homomorphisms from Z to Z/2Z - Help Needed
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Undergrad Cartesian scalar equation of plane
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Graduate Elliptic Curve y^2 = x^3 +17; show N_p = p
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Graduate How to prove that the dim of two subspaces added together equals dim
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