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.
Undergrad The Odd Only Spiral (A twist on the ulam spiral with an interesting property)
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MHB How Do Sets W, Y, and Z Intersect?
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High School How can I solve equations by rearranging them?
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Graduate Relationship between eigenvalues and matrix rank
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MHB Find the Inverse of a Vector: Solve for x in Terms of b
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Undergrad Linear independance and span (Definition)
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Graduate So, no prefixes...Do planes in higher dimensions satisfy Euclid's definition?
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Graduate Help me understand the inductive solution to the lines in the plane problem?
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Undergrad Nonhomogeneous system of linear equations
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Graduate A question about definition of a category
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Graduate Homogeneous least squares
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Graduate Is (n+1)(2n+1) Always a Multiple of 6 for All Natural Numbers n?
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Graduate Proving one element in the symmetric group (s>=3) commutes with all element
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Undergrad About vector space and subspaces
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Graduate For separable extensions, why may we argue as if they're finite?
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Undergrad How to prove a function is vector valued
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Undergrad Transformation Matrix from x-axis
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Graduate Determine optimal vectors for least squares
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Graduate Counting Theorem: Creating Squares w/ 8 Equilateral Triangles
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High School Dimension of the circle in the plane is 1
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Graduate 2^k+1 never divisible by u(8x-1) in integers
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Graduate Eigenvalue Solvers for Structural Dynamics
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Graduate Determinant of symmetric matrix with non negative integer element
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Graduate Is the Determinant of a Symmetric Matrix with Zero Diagonal Elements Non-Zero?
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Graduate Proving Adjoint of an Operator in Hilbert Space: Common Mistakes Explained
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Graduate Prime Ideals: Abstract Algebra Example
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Undergrad Finding basis of a column space/row space
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Graduate Understanding the Normalization of Pauli Matrix in Quantum Mechanics
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Undergrad Find if Parametric equations are perpendicular
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Graduate How to rotate a 3D complex vector?
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Graduate Some basic question about a quotient ring
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Undergrad Are There Relationships Between the Column Vectors of a Matrix and Its Inverse?
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Graduate Proving the Relationship between Operators on a Finite-Dimensional Space
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Graduate Are There Ordered Fields Beyond Real Numbers and Rationals?
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Graduate Why is x^p - a irreducible over a field of characteristic p?
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Undergrad Positive definitive matrix in wikipedia
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Graduate Demonstrating that (im τ) \cap (ker τ) is the Zero Space
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Undergrad Can the Angle Between Two 7-Dimensional Vectors Be Calculated?
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Graduate Can a Non-Zero Tensor Product of Modules Be Zero?
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MHB Finding elements in a quotient ring
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MHB Proving Z[√(-3)] is not a euclidean domain
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Graduate A way to express scalar triple product from inter-vector angles?
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Graduate Nonzero divisor in a quotient ring
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MHB What Are the Units in the Ring $\mathbb{Z}[\sqrt{-7}]$?
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Graduate Multiplication of incompatible matrices
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High School Incredibly simple question about the logic behind systems of equations
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Graduate Efficiency and the Euclidean Algorithm
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MHB Finding the units in the ring F[x]
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Undergrad Inverse of Lower Triangular Matrix
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Graduate About the number of irreducible elements in UFD ring
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Graduate The Asymtotic Eiegen Values of a Circulant matrix
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Graduate Dimension formulas for Lie algebras
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Maximizing Your Tips and Tricks for Focusing on Key Elements
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MHB Finding All $2\times 2$ Matrices That Satisfy $A^2=A$
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Undergrad Can a Field Also Be a Vector Space?
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Graduate What is meant by can be identified with
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Undergrad Determinats,dependence, span, basis.
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Graduate Capturing n basis vectors by single one
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Graduate Galois Theory: Degree of Q(ω)/Q & Why 6 Basis Vectors?
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MHB Recommendations for a Massive Algebra Text
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MHB What is the Correct Method to Determine the Coplanarity of Vectors?
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Undergrad Is a vector in a vectorspace its own projection onto that vectorspace?
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Graduate When solving a linear system for x and y, am i in a group? ring? field?
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MHB Algebraic Structure to solve a linear system of 2 variables?
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Graduate Eigenvalue of overlapping block matrix
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Graduate How Does Modular Arithmetic Prove Divisibility by 17 in Number Theory?
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Graduate Solutions to Polignac's and Twin Prime's Conjecture
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Undergrad How can a basis in a vector space be used to determine linear independence?
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MHB Solving Matrix Norms & Finding Valid Expressions: Help Needed!
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Graduate Is H X-s-permutable in N Given X May Not Be a Subset of N?
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Graduate Quotient groups of permutations
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MHB Find polynomials in S, then find basis for ideal (S)
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Graduate Find Best Combinations of Non-Overlapping Matrix Elements
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Undergrad What Are the Requirements for a Subset to Be Considered a Subspace?
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Graduate Ring Theory: Eisenstein's Criterion & Z[x]/pZ[x]
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Graduate Combining two sets of regular sequence
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Graduate Subfields of finitely generated algebras
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Graduate Prove Eigenvalue λ=0 is Only Solution to Ax=0 for All x
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Undergrad How do you tell what a vector space will look like from it's spanning set.
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Graduate What symbol is used for linear operator actions?
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Undergrad Reminder on how to find eigenvectors
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Undergrad [Numerical] Why is it better to solve Ax=b instead of calculating inv(A)
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Undergrad How to Find the Sum of Roots of the Polynomial \( x^{100} - 3x + 2 = 0 \)?
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Undergrad What is an Integral Solution in Equations?
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Graduate Upper Hessenberg zero-column sum matrix
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Undergrad Inverse of Matrix - Product Form
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Is this the perfect outfit for an Abstract Algebra class?
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Graduate Is an infinite series of random numbers possible?
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Graduate How Accurate Are the Bounds for Eigenvalues in Circulant Matrices?
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Graduate Product of Ideals makes no sense to me
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Graduate Why <v,v> >= 0? Understanding Inner Product Definition
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MHB Polynomial of degree 3. splitting field.
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Undergrad Characteristic equation formula for a nxn matrix ?
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Undergrad Difference between an eigenspace and an eigenvector ?
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Graduate What is the Lower Bound for the Determinant of a Circulant Matrix?
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Graduate General question about orbits (group theory)
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Graduate How do you evaluate a norm like this?
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Undergrad What went wrong with my solution for a damped mass spring system?
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Graduate How to find the plane at which two hyperplanes intersect.
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Graduate Vector space or inner product space - ambiguous
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