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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 First Weyl Algebras .... A_1 ....
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MHB First Weyl Algebras .... A_1 ....
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MHB Understanding Bresar's Example 1.10 on Simple Matrix Rings: Can Anyone Help?
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Undergrad Introduction to Simple Matrix Rings in Noncommutative Algebra
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Undergrad N-Dimensional Real Division Algebras
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MHB How should this matrix be multiplied
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MHB Subgroups of the dihedral group D6
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MHB Proving Determinant of Mirror-Image Identity Matrix
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MHB How can we compute the Galois group of a subgroup of a splitting field?
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Undergrad Frobenius Theorem - Bresar, Theorem 1.4 ....
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Undergrad Validity of proof of Cauchy-Schwarz inequality
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MHB Inverse of Giant $7 \times 7$ Matrix: Tips & Tricks
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MHB Permutation question concerning cycle shapes
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MHB Frobenius Theorem - Bresar, Theorem 1.4 ....
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MHB Finding 3 natural numbers by the rule of Sarrus
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Undergrad Bresar, Lemma 1.3 - Real Quaternions .... Division Algebras
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Undergrad Bresar, Lemma 1.2 - Finite Division Algebras ....
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Undergrad Linear Algebra: characteristic polynomials and trace
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Undergrad Another Question about Finite Dimensional Division Algebras ....
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MHB Show that the set of the upper triangular matrices is a ring
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MHB Finite Dimensional Division Algebras - Bresar Lemma 1.1
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Undergrad Finite Dimensional Division Algebras - Bresar Lemma 1.1
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Undergrad First Sylow Theorem: Group of Order ##p^k## & Cyclic Groups
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MHB Determining when a system of equations has no solution and infinite solutions
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Undergrad A regular matrix <=> mA isomorphism
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Undergrad Unitary Matrix Representation for SU(2) Group: Derivation and Verification
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Graduate Understanding the Cost Function in Machine Learning: A Practical Guide
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High School Is identity matrix basis dependent?
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MHB The extension is Galois iff E is a splitting field of a separable polynomial of F[x]
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Undergrad What Does the Mysterious Symbol in a Formal Proof Represent?
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MHB Is This Matrix Idempotent?
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MHB How Do You Calculate Ore Production and Costs for Zinc and Aluminium?
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MHB Index of Positivity in Quadratic Form: $f(X) = \sum^{n}_{i=1} x_{2}^{i}$
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MHB Is there a more efficient way to determine the basis of a subspace?
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MHB Dimension of Dirac Functionals in $V$: Find the Answer
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Graduate Quaternions: Extension of Real Numbers?
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MHB The extension is Galois iff H_i is a normal subgroup of H_{i-1}
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MHB Can the vectors be written as a linear combination?
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Undergrad From Non Hermitian to Hermitian Matrix
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MHB How Does Eisenstein's Criterion Confirm the Irreducibility of a Polynomial?
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Graduate (sum to infinity of divisor function)^{2} -- simplify the expression
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MHB Solve Exponential Fraction Equation for $α$ ($C$, $m$)
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Graduate Modular Forms: Non-holomorphic Eisenstein Series E2 identity
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MHB Show that the mapping is surjective
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MHB How to Prove Galois Extension Statements in a Normal and Separable Field?
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MHB How Can We Geometrically Describe Vectors Orthogonal to the Vector $(-4,1,-3)$?
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High School Understanding the Dagger Notation in Quantum Mechanics
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Undergrad Representing vectors with respect to a basis
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Undergrad Rotation Matrix for Vector v=(a,b,c) by Angle θ | Efficient Computation Method
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MHB Are Mutually Perpendicular Vectors Always Linearly Independent?
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Undergrad Why Is the Ratio of y2/y1 Not Constant for Linearly Independent Vectors?
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Undergrad Linear regression on data collection error
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Undergrad Orthogonal basis to find projection onto a subspace
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MHB Is Each Extension of Degree 2 Normal?
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Undergrad Normalizer of a subgroup of prime index
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Undergrad Artinian Modules - Bland - Proposition 4.24
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MHB How can I prove the rank of a matrix with a specific pattern of entries?
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High School How do we obtain a Taylor expansion of a non-linear functional?
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Undergrad Example from Bland - Right Artinian but not Left Artinian ...
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MHB Example from Bland - Right Artinian but not Left Artinian ....
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Undergrad What is the meaning of N(H) in subgroup notation?
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MHB Proving Positive Definite Scalar Product for $n \times n$ Matrices
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Undergrad Solving simultaneous equations with matrix
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MHB Example from Bland - Right Noetherian but not Left Noetherian
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Undergrad Example - Bland - Right Noetherian but not Left Noetherian
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Undergrad Eigenvectors for degenerate eigenvalues
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MHB Question for null space of a matrix
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Undergrad Standard Free Right R-Module on X - B&K Section 2.1.16
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MHB The irreducible polynomial is not separable
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MHB Why Are My Gram-Schmidt Results Different on Wolfram|Alpha and MATLAB?
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Undergrad Factorization of a matrix equation
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Undergrad Is the set {e^x, x^2} linearly independent?
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MHB Finding a 3rd polynomial to create a basis.
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Undergrad How to prove that shear transform is similarity-invariant?
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MHB Splitting Field of $g$ over $F$?
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Graduate 3dim Poincare Algebra - isl(2,R)
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Undergrad Motivation and proof behind cross products
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Undergrad The Relationship Between Rank and Elements in a Jacobian Matrix
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Undergrad What does adjacent indices mean in the context of matrix multiplication?
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MHB Finding B^-1 in 3x3 Matrices with Linear Algebra
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Graduate How Do Engel and Lie Arise Naturally?
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MHB Some basic question about vector spaces
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Undergrad Matrix Notation: ℝm x n Meaning & Vectors
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Undergrad Basic Question about a Ring Homomorphisms
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Undergrad Is Every Isomorphism in Vector Spaces Reflexive?
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MHB Proving Convexity: Steps and Conditions for a Set to be Convex
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Undergrad Are There n!/2 Even/Odd Permutation Matrices for nxn?
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MHB Basic Question on Ring Homomorphisms
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Undergrad Proving Matrix exponential property
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MHB The splitting field of f over F is also the splitting field of f also over E
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MHB Zero matrix with non-zero above diagonal
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Undergrad Understanding r^t & a: Seeking Clarification on Raman Spectra
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Undergrad Matrix Rings - Basic Problem with Meaning of Notation
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MHB How Do You Interpret Rowen's Notation in Matrix Rings?
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Undergrad How Do Elementary Operations Affect Matrix Rank Preservation?
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High School Matrix A^(m+1) is different from A^(1+m)?
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Undergrad Existence of basis for P_2 with no polynomial of degree 1
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MHB Noetherian Modules and Submodules - J A Beachy, Proposition 2.4.5 .... ....
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Graduate Algebra - Clifford, Dirac, Lorentz
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Graduate How Do Ladder Operators Annihilate States in SU(2) Algebra?
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