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 Category Theory - Initial and Final Objects
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MHB What Are the Eigenvalue Properties of Hermitian Matrices in Quantum Mechanics?
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Graduate Double Summation Result: \alpha^i\alpha^j
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Graduate What is the Standard Definition of a Tensor Product of Two Vectors?
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MHB What Are the Coefficients in Aluffi's Monoid Rings?
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MHB Lie Algebras and Similarity Transformations
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Graduate Abstract Algebra: Dummit and Foote Exercise
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MHB Eigenvectors of 2*2 rotation matrix
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Graduate Proving the adjoint nature of operators using Hermiticity
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Undergrad Linear dependence of two vectors
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MHB Creating a Unit Vector after Gram Schmidt Process?
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Undergrad What is a Centered Difference Matrix?
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Graduate Diagonalising an n*n matrix analytically
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Monday Giggle, Dear Algebra ....
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Undergrad How does row operation on an augmented matrix result in the inverse of a matrix?
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Undergrad Solving System of Nonlinear Equations (x,y,z)
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Graduate Passive and Active Transformations
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Graduate Use FMM or FFT for low-discrepancy sample of atoms?
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MHB Solve System of Equations: Find x, y, z & l1, l2, l3
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Graduate Subgroups of Symmetric and Dihedral groups
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Graduate Prove relation between generators and automorphisms of Z/nZ*
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MHB Matrix Ops: R(x)v & R(x)w Rotate Counter-Clockwise
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MHB Finding eigenvectors for a double root
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Undergrad Are Both Eigenvectors Correct?
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High School Can someone explain to me what a matrix is in simple words?
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MHB Can a Matrix be Written as a Linear Combination of Another Matrix's Columns?
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Undergrad Tips for proof based linear algebra?
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Graduate Understanding the isomorphism theorems
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MHB Proving Ideal Property of f(x)=0 for Every Rational x in $\mathcal{F}(\mathcal{R})$
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Undergrad Reason for just a 0 vector in a null space of a L.I matrix
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Graduate How to formulate nonsingularity of matrix (I + A*B) in LMIs?
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MHB Is there a contradiction in assuming that $J$ is linear over $C^1([a,b])$?
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MHB Are the Weak and Strong Norms Correct for These Function Distances?
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Undergrad Area of figure, resulting from unit square transformation
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Undergrad Having difficulty working out a Char. Pol. for Eigenvalues
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Graduate Non-Commutative Hilbert Nullstellensatz?
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MHB Determinant using gaussian elimination
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Graduate Irreducibility of polynomial (need proof evaluation)
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Graduate Linear Algebra; Transformation of cross product
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MHB Can $\mathbb{Z}[\sqrt{-3}]$ Be Proven as a Principal Ideal Domain?
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Graduate The complex algebra graded by Z-2
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Graduate Intersection of line and surface
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MHB Understanding Extension of Scalars in a Vector Space
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Graduate Dual spaces and the meaning of "Dual"
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MHB What Are Some Alternative Sources for Help with Lie Algebra Definitions?
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Graduate When do roots of a polynomial form a group?
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Graduate Commutator of the matrices of the rotation group
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Undergrad Finding if two sphere's intersect method
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Graduate Cosets of Monoids: Conditions for Partitions
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Graduate What does Hilbert's Satz 90 mean?
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Graduate Determinant and symmetric positive definite matrix
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MHB Kernel on linear transformation proof
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Graduate Linear Transformations and matrix representation
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Graduate Find minimum number of generators for Z/nZ
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Graduate Finding number of automorphisms for Z/nZ^*
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Graduate Why is Force Physically Interpreted as a 1-Form in Line Integrals?
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Graduate What Are the Differences Between Group and Algebra Terminology?
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Graduate Matrix with fractions for indices?
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Graduate Understanding proof that ##(A^T)^{-1} = (A^{-1})^T##
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How Can I Overcome My Dislike for Linear Algebra Before the Exam?
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Graduate Can a Projection Be an Isomorphism If It Maps to a Proper Subset?
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Graduate Why Do Engineers Use Pullbacks and Pushforwards in Mathematics?
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MHB How Can I Derive a Contradiction from This Mathematical Statement?
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Graduate Tensors with both covariant and contravariant components
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Graduate Why Is Isomorphism Confusing in Linear Algebra?
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Undergrad Solving Row Echelon Form: Practicing Tips for Students
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Graduate Understanding Rotation Matrices: A Journey of Mistakes and Lessons Learned
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MHB Conjugating Subgroups: Proving |X_K| Divides |K|
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Graduate Cross product in arbitrary field
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Graduate Singular spectral analysis of periodic series with period L
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MHB Vectors and their derivative proof
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MHB Understanding the Role of Abelian Cartan Subalgebras in Simple Lie Algebras
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MHB Plane that is tangent to two curves at an intersection
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Undergrad If A is triangular and no entry on the main diagonal is zero
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Graduate Trying to understand notes, any feedback is appreciated
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Graduate How to solve a very large overdetermined system numerically?
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Graduate Least squares parameter correlation
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MHB Confusion about the notation of transpose
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MHB Field extensions and roots of polynomials
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Graduate Short Exact Sequence: Explaining C = B/A
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Undergrad Matrices: Rows and Columns Meaning
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Graduate Why is the bi-linear bracket operation on a one-dimensional Lie algebra abelian?
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MHB How Can I Determine if Two Lie Algebras are Isomorphic?
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Graduate What is more efficient, autocorrelation or SSA?
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MHB Confusion about the Killing form for A1
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Undergrad How Do You Convert ENU to ECEF Coordinates?
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Graduate Grouping constrained optimization
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MHB Basis Theorem for Finite Abelian Groups
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Graduate Fundamental Theorem of Field extensions
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Graduate Polynomials over a ring evaluated at a value?
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Undergrad Is xTAx always non-zero for a real, symmetric, nonsingular matrix A?
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Graduate SVD of a reduced rank matrix still has non-zero U and V`?
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MHB Find Min Polynomial of $\alpha$ Over $\mathbb{Q} | Solution Included
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Graduate Symmetry of Orthogonally diagonalizable matrix
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Undergrad Linear Combination Mapping: Is the Invertible Matrix Theorem True or False?
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Graduate Can the Set R(G) be Proven as a Ring in Convolution on Groups?
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Graduate Vector subspace and linear transformation
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MHB Homomorphism - Sharper Cayley Theorem
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MHB Finding Isomorphisms between Groups: D6, A4, S3xZ2, G
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Graduate Book for abstract algebra (group and galois theory)
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