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 Understanding the Relationship between Non-Members in Generated Subgroups
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What is the length of the vector (1,i) and why can it still be normalized?
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How Do You Correctly Multiply Complex Numbers to Verify Roots?
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Finding eigenvectors of a matrix that has 2 equal eigenvalues
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If A is a tridiagonal Matrix , what does this mean ?
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Matrices satisfying certain relations
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Is the dimension of two vector spaces the same if they have equal cardinality?
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Transpose a matrix whose elements are themselves matrices
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It is defined that for any matrix A, [itex] A^{0} [/itex] is defined
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Trying to find a simpler way to calculate this function
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Matrix Alalysis, Matrix Algebra, Linear Algebra, what's the difference?
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Why is that Nullspace of A is subset of nullspace of A^T*A
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How Is an Inner Product Defined on an Abstract Vector Space?
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MHB If X is a subset of G such that xy = yx for all x, y in X, then <X> is Abelian.
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Eigenvectors and eigenvalues - how to find the column vector
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Explicit expression for inverse of I-A
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Does [itex]A^T A[/itex] have an inverse?
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Example of Commutative but Not Associative Binary Operation
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Powers of matrices equal to the identity matrix
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MHB Finding Composition Series of Groups
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What is a number, and what is it made of?
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Are Matching Commutation Relations Enough to Prove Lie Algebra Isomorphism?
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A Conjecture on the Collatz Conjecture
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Symmetrical Matrices and Invertibility: Is A Always Invertible If Ax ≠ Ay?
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Solve Problems with Gaussian Random Matrix: Compressed Sensing Senior Project
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Transformation matrix of linear n-dimensional state-space system
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Do you prefer Topology or Algebra?
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How to Check for a Non-Abelian Group of Order 21 Using Basic Techniques
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Fermat Numbers - Factor Form Proof
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Need proof re prime of the form 8N +/-1
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Finding a Matrix that is Similar to A=[1 1;0 1]
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Actions of Field on Vector Space
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MHB How can I prove that the homomorphism defined by f(gH)=gJ is well defined?
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A lemma in the integers from calculus
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Reduced row echelon form of a square matrix
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The Cantor-Schreuder-Berstien theorem
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Determinant - best way of introducing determinants on a linear algebra course
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Quantum algorithm for order finding
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Are the orders of Aut(G) and Inn(G) infinite for an infinite group G?
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Splitting field with Galios group A4
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How do congruences work in mod arithmetic?
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Function Fi Help: Simplifying the (m,n)=d Demonstration
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Proving an inequality for order finding
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Is a Group Homomorphic under Multiplication if it is Not Under Addition?
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Show that a set of functions is linearly independent
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How Can the Dual of V in Terms of Z and W Be Expressed?
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How to Find an Explicit Description of a Plane from an Implicit Equation?
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Is the Function f(x) Multiplicative for Modulo and Prime Numbers?
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Understanding Direct and Inverse Limits
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Prove the set of integers is a commutative ring with identity
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What Do C[T]B and B[T]B Mean in Linear Transformations?
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MHB Question about generators and relations.
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Number of subgroups of a group G
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What Matrices Commute with a Diagonal Matrix with Distinct Eigenvalues?
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What is the Significance of Subspaces in Linear Algebra?
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MHB Is this operator diagonalizable？
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Function to generate linearly independent vectors
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Sum_{k=0n} p(k) where p(k) = number of partitions of k
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Simplifying E=mc²: Tips and Tricks for Solving Equations
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MHB Transforming Vectors: Real-Life Examples Beyond Inclined Planes
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Vector Spaces Help: Definition & Meaning
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Line maximizing orthogonal projections
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Understanding Mappings: Injective, Surjective, and Homomorphisms
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Is a set with a 0 vector linearly independent?
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MHB Factorization of Polynomials - Irreducibles - Anderson and Feil
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A question on invertible matrixes
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Lattice Points on Circle: Determining the Number of Points on the Boundary
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Eigenvalues and characteristic polynomials
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Number of vectors needed to Span R^n
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Goldbach Conjecture: Relationship to Even Numbers
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Linear Algebra- Onto and One to One Linear Transformations
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What Is the Inner Product <V,s> in Complex Vector Projections?
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What Are the Axioms and Identities for Two-Dimensional Lie Algebras?
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Building a rotational matrix transformation
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MHB Rank & Nullity: 3x3 Matrix w/ Plane Origin & LD Vectors
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What is the basic assumption behind the Cauchy-Riemann equation?
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MHB Linear Transformation (Fredholm Alternative Theorem)
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MHB Matrix Transformations from R^n to R^n
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MHB Dynamical Systems and Markov Chains
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MHB Row Space, Column Space and Null Space
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MHB Where is the Mistake? Solving a System of Equations
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Is There a Standard Notation for Matrix Rows and Columns?
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What Is the Physics Intuition Behind a Complex Vector in a Linear Space?
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Eigenvalue Q: What if ##\lambda=0##?
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How Does Re[s]>0 Relate to Laplace Sine Transform Conditions?
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Several matrix inverse properties
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MHB Abelian Groups of Order $2100$: Elements of Order $210$
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Proof that there exists a smallest positive linear combination?
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Inner Automorphism: Clarifying Notation Confusion
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Can Order and Size be Equivalent?
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MHB Automorphisms of an extension field
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MHB Infinite dimensional vector space
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A'A and A have the same null space
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Does a Closed Form Exist for the Harmonic Series?
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How Do We Calculate the Diagonalize Matrix of a 3x3 Matrix?
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MHB Linear Algebra and Determinant
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MHB Solving Congruences with Polynomials: A Prime Challenge
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What is the best way of describing isomorphism between two vector
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FLT Theorem: No Solution for a^p + b^p = c^p, p > 2 | Image Included
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Pells equation for D prime and =n*n-3
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