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.
MHB Finding All $2\times 2$ Matrices That Satisfy $A^2=A$
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Can a Field Also Be a Vector Space?
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What is meant by can be identified with
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Determinats,dependence, span, basis.
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Capturing n basis vectors by single one
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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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Is a vector in a vectorspace its own projection onto that vectorspace?
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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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Eigenvalue of overlapping block matrix
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How Does Modular Arithmetic Prove Divisibility by 17 in Number Theory?
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Solutions to Polignac's and Twin Prime's Conjecture
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How can a basis in a vector space be used to determine linear independence?
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Is H X-s-permutable in N Given X May Not Be a Subset of N?
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MHB Find polynomials in S, then find basis for ideal (S)
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Find Best Combinations of Non-Overlapping Matrix Elements
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What Are the Requirements for a Subset to Be Considered a Subspace?
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Ring Theory: Eisenstein's Criterion & Z[x]/pZ[x]
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Subfields of finitely generated algebras
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Prove Eigenvalue λ=0 is Only Solution to Ax=0 for All x
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How do you tell what a vector space will look like from it's spanning set.
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Reminder on how to find eigenvectors
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How to Find the Sum of Roots of the Polynomial \( x^{100} - 3x + 2 = 0 \)?
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What is an Integral Solution in Equations?
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Upper Hessenberg zero-column sum matrix
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Inverse of Matrix - Product Form
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Is this the perfect outfit for an Abstract Algebra class?
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Is an infinite series of random numbers possible?
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Product of Ideals makes no sense to me
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Why <v,v> >= 0? Understanding Inner Product Definition
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MHB Polynomial of degree 3. splitting field.
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Characteristic equation formula for a nxn matrix ?
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Difference between an eigenspace and an eigenvector ?
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How do you evaluate a norm like this?
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What went wrong with my solution for a damped mass spring system?
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How to find the plane at which two hyperplanes intersect.
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Vector space or inner product space - ambiguous
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Cartesian equation of plane using two lines?
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What is the significance of the zero vector in a vector space?
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How Do You Determine the Maximum Order of an Element Modulo n?
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Dimension of a Set of Transformations
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MHB Find Center of Groups of Order 8
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Does the following point lie on plane?
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Finding out a equation of a plane that is parallel to a plane
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Is There a General Way to Format a Counterexample for Diagonal Matrices?
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Sylvester's Criterion for Infinite-dimensional Matrices
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Linear Transformations and Bases
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MHB How Many 3x3 Non-Singular Matrices Exist with Four 1s and Five 0s?
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Confusion: computation of class number of K=Q(sqrt(30))
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Understanding the Ideal Class Group of Q(√-17)
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How to interpret absolute value bars?
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Galois Groups of Extensions by Roots of Unity
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Combinatorial Number Theory Problem
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Confused with working out the span of a set of vectors in R^2
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How to know if an infinite system of linear equations has a solution
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MHB What is the Complete Set of 2x2 Matrices Satisfying $A^2-4A+3I=0$?
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Finding a basis for the following vectors.
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Equal Distances Between N Points in R^n-1+ | Solving System of Equations
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PA=LU decomposition (w/ Partial Pivoting)
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Algebraic multiplicity of matrix
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How to make matrix positive definite (when it is not)?
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Is the Number of Free Variables Constant in Echelon Form Systems?
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What are Ideals and Polynomial Rings? A Simple Explanation and Concrete Example
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Help Develop Tongue in Cheek Abstract Algebra Proof
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Maximum inner product between two orthgonal vectors (in standard dot procut))
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Show that two polynomials cannot span P2.
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Group representations, interesting aspects?
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Finding the basis for a set of vectors.
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Writing a matrix as sum of a constant * matrix
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Solving Quadratic Diophantine Equations with A=0, C=0
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Linear independence of sin (x), cos (x) and 1, proof
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Zeroes at the end of a FACTORIAL
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Finite Reflection Groups in Two Dimensions - R2
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So is chike obo proof of fermat's last theorem
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Proving 2-Norm of A: Understanding the Relationship Between u and v
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Field extension, properties,proof
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Are e and π Transcendental Numbers? Investigating the Rationality of e + π
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How to calculate powers of a 2x2 matrix WITHOUT eigenvectors ?
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Proving Jordan Canonical Form for Similarity of Matrices with Same Polynomials
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Computing a kronecker product of two matrices
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Finding Real Solutions for x-tanh ax = 0 with a>1
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Does d dividing n imply phi(d) divides phi(n)?
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Question on subspaces and spans of vector spaces
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Offset between non-homogeneous and homogeneous recurrence sequences
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Aligning a matrix with its eigen vectors and other questions?
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Jordan Normal Form & Generalized Eigenvectors
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Induction Method: My Question About Theorem in Finite Groups
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How to learn to like number theory
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Eigenvalues of the product of two matrices
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Understanding Vector Products - Mike's Query
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Mertens function : new formulation
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Help me understand a line in an ATA is positive, semi-definite proof
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Matrix Multiplication to translate object with given vertices
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Proving that the parity of a permutation is well defined.
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Factorize x^2 - z*y^2 with Gcd(x,y)=1, Gcd(x,z)=1, Gcd(y,z)=1, and z squarefree
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Eigenvalues & Eigenvectors: Repeated vs Distinct
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Expressing matrices as outer product of two vectors
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Putting a matrix into Rational Canonical Form
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