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 Is subtraction an operation on Z?
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MHB How can we prove that the center of a ring is a subring?
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MHB Does $(A^T)^2=(A^2)^T$ for $2\times 2$ matrices?
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MHB Unit of Ring Question - Cbarker1
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MHB Matrix Operations: Solving for A+B, AB, BA, AC, and CA
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MHB E2.3 Express T_b^b as the product of three matrices
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Graduate Block Diagonalization - Representation Theory
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Insights Lie Algebras: A Walkthrough - The Structures
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Insights Lie Algebras: A Walkthrough - The Basics
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Undergrad Can the cross product concept be completely replaced by the exterior product?
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Undergrad Confused about Gauss's Lemma of Irreducibility
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Undergrad Understanding the cross product and rotations
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MHB Find an A and b such that Ax=b has the solution set......
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MHB Can You Prove These Properties of Normal Subgroups in Group Theory?
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Definition of Finite Field: Addition and Multiplication Groups
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Graduate How to find the Jordan Canonical Form of a 5x5 matrix and its steps?
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Undergrad Smolyak reduced grid for three dimensions
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Graduate Structure of modulo-integer matrix group GL(r,Z(n))?
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Undergrad Don't understand proof of uniqueness theorem for polynom factorization
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Undergrad Matrix Decomposition Explained: Simple Illustration
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Undergrad The dimensions of locus that is intersection of loci
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Undergrad Stewart's Galois Theory doesn't make sense
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Graduate Highest weight of representations of Lie Algebras
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Undergrad Can Fundamental Theorem Algebra be proven by simple DOF?
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Undergrad Has it been proven that quintic equations cannot be solved by *any* formula?
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Undergrad Markov Process: How to Tell Reversibility & Eigenvalues=1
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Undergrad What's the difference between a ring and a field?
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Undergrad Is the identity of a group unique?
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MHB 25.3 Find the Jordan Normal Form of A
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High School Why Are Determinants Considered Outdated in Modern Linear Algebra?
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Undergrad Block Diagonal Matrix and Similarity Transformation
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MHB 290 Expanding this determinant about the the second column....
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MHB 25.1 find all possible Jordan Normal Forms of A
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MHB Are the Vectors S and T in the column of (ABC)
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Undergrad Dot product definition: deriving component form
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MHB Symmetric/Alternating k-linear functions, Wedge Product
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Graduate The product of a matrix exponential and a vector
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Undergrad Vector Space of Alternating Multilinear Functions ....
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High School Finding Bases for Row and Column Spaces
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MHB Show that dim(Ker(SoT))<=dim(KerT)+dim(KerS)
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MHB Find $\left[T\right]_\beta^\beta$ for NMH{823}
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High School Composition of elements of SO(4)
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Undergrad How to Determine N from Refraction Angles and Constants?
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MHB What is T_alpha^beta in matrix form using e1 and e2?
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MHB So V is not vector over field \Bbb{R}
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MHB (2s+3)([x y]) not sure exactly what we are supposed to do with the 3
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MHB Linear Algebra Rank of a Matrix Problem
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MHB What Is the Basis for the Kernel of the Differential Operator \(D^4-2D^3-3D^2\)?
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MHB 11.3 Give the matrix in standard basis
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MHB Homework: 13s: Critical Thinking Challenge
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MHB Tech Troubleshooting: Starting with Your Cell Phone
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MHB What are the linear operators S and T?
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MHB 13 is a linear transformation and .......Determine T
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Undergrad Relation Between Cross Product and Infinitesimal Rotations
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Undergrad Invariant symbol implies existence of singlet representation
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MHB 10.1 are linear independent ....
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MHB Need some hints on my HW about Linear functionals
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MHB Proving a Subset of a Group is a Group
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Undergrad Anyone familiar with Compressive Sensing (sampling)?
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Undergrad Affine hull and affine combinations equivalence
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MHB Showing the Dual Basis is a basis
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Undergrad What is Kronecker's theorem/lemma for root solutions?
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MHB Check the statements about a 4x5 matrix with rank 2.
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High School How do I improve my proof writing style?
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Undergrad Proving Commutator Identity for Baker-Campbell-Hausdorff Formula
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MHB Null Space of A: Find Rank & Dim.
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MHB What is the determinant of the identity matrix in a larger matrix?
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Undergrad When is a subset a subspace in a vector space?
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MHB E1.4b Determinant with zero column
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Undergrad Proving the Orthogonal Projection Formula for Vector Subspaces
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Graduate Particle swarm optimization for matrix inversion
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MHB Verifying $\beta$ as a Basis of $\Bbb{R}^2$ & Finding $|v|_{\beta-}$
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MHB Graded Algebra: Understanding Color Dirac Spinors in Space-Time
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Undergrad Determining if the system is consistent
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MHB Proving General Associativity for Group by induction
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MHB Proof the set with the multiplication is a group
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MHB Matrices of Linear Transformations .... Poole, Example 6.76 ....
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Undergrad How to Write a Matrix on a Webpage?
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MHB Determine vec {{x},{y},{3x+2y}} in R^3 form a vec space
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MHB Is This a Valid Vector Space with Unusual Operations?
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Undergrad Can't understand a step in an LU decomposition proof
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MHB Matrix Addition: OK - No Examples Found
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MHB Is a Group Abelian if Inverses Commute?
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MHB Is the Kernel of Trace Equal to the $F$-Subspace of $V_\sigma$?
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Graduate Quaternions and Video Game Design
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MHB A and solution are known find B matrix
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Insights Lie Algebras: A Walkthrough - The Representations
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MHB What is the determinant of the given matrix and why do the scalers change sign?
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MHB Is A Invertible When Each Diagonal Element is Nonzero?
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MHB Find $(AB)^T$: Calculate Matrix Product & Transpose
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MHB Linear Combination - missing data ?
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MHB 5.2 another Ax=B with an inverse
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MHB Are These Sets Vector Subspaces of R^3?
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MHB What is the solution for x in the equation 1.4x + 9 = -2?
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Graduate Why does the Lie group ##SO(N)## have ##n=\frac{N(N-1)}{2}## real parameters?
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MHB Combination of Linear Transformations
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MHB Dual Spaces .... Friedberg et al, Example 4, Section 2.6
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MHB A question about surjective module-homomorphisms
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MHB Matrices- conditions for unique and no solution
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Undergrad Orthogonal transformation and mirror transformation
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