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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.
Graduate Is Matrix Addition Commutative?
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High School Modulus & Division: Last Digit of Numbers Explained
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MHB Can every subring of an algebraic extension be a field?
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Graduate How do I make a change of basis with tensors in multilinear algebra?
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Graduate Iterations of functions of noncommutative variables
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MHB Dimension and Basis of a Relation in R5
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MHB Find the coordinates of the expression
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MHB Find coordinates of f′, f′′, f′′′ in the basis
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MHB Showing Linearity of $\varphi$ for $K(a)$
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MHB Can a Group Have a Trivial Automorphism Group with Less than Three Elements?
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MHB What Is the Splitting Field for \(x^{p^{80}}-1\) Over \(\mathbb{F}_p\)?
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MHB Field extensions and degree of odd prime numbers
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Undergrad Why equating two planes does not provide solutions?
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Graduate Artin - domains don't seem to match
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Graduate Eigenstuff of Second Derivative
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Graduate Pfaffian and determinants of skew symmetric matrices
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Undergrad Line operations on matrix products
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Undergrad Defining a vector in magnitude,angle form.
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Graduate Are the Functions Linearly Independent Based on the Matrix of Their Outputs?
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Undergrad Line of intersection of two planes
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High School Finding determinant through Gaussian elimination
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Graduate Solving the Inversion Problem with RGB Filters
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Graduate Is the Klein Four Group Identical to the Dihedral Group D2?
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MHB How can I prove that $\theta_p$ is a p-Norm?
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Graduate Associativity of Hadamard and matrix product
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Graduate Length-Norm inequality to root-n times Length (using 2|uv| <= |u|^2 + |v|^2)
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Undergrad Why is det(C)=det(A)^(n-1) for cofactors and determinants?
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MHB Let F ={0 , 1 , a , b} be a field with four elements.
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Undergrad Proving Non-Trivial Solutions of Ax = b
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MHB Units of the set of all Eisenstein Integers
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MHB Ring of integer p-adic numbers.
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Undergrad Proving Determinant of Matrix Unchanged by Adding Columns
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MHB Show that Q adjoin square roots of 2, 3 is a vector space of dimension 4 over Q
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Graduate Groups of homomorphisms of abelian groups
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MHB Showing that $A$ is an Ideal of $\mathbb{Q}[x]$ and Expressing it as $<f(x)>$
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MHB Units of the Gaussian Integers, Z[i]
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Graduate Is intuition more important than logical proof in mathematics?
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Graduate Can you explain the determinant formula using permutation notation?
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MHB Every submodule has at least one set of generators?
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Graduate Does the inverse of this special matrix have a power series expansion?
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Graduate Is the Canonical Basis in Mathematics Just a Useful Convention?
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Graduate Properties of Kernels of Homeomorphisms
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MHB What is the Proof for the Nonempty Intersection of Submodules Being a Submodule?
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MHB Why must the ring $K[x]$ have infinitely many irreducible polynomials?
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Undergrad Transform Cylindrical coordinates into Cartesian Coordiantes
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MHB The polynomial is irreducible iff the condition is satisfied
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Graduate Explicit construction of isomorphisms of low-rank Lie algebras.
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MHB Problem Regarding Left Unital Artinian Ring (set by Euge)
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MHB Field extension-degree of the minimal polynom
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MHB Ordered Index Sets for Direct Sums & Products of Modules: Explained by B&K
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MHB Prove that the order of 5 modulo 2^k is 2^(k-2)
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MHB Direct Sums of Copies of Modules - B&K - Exercise 2.1.6 (iii)
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MHB Show the Units of Zn with modular multiplication are a group
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MHB Finding Notation for Left Invariant Vector Fields on Lie Groups
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Graduate Function scales eigenvalues, but what happens to eigenvectors?
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Undergrad Finding Inverse of Matrix by using Gaussian-Jordan Elimination
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MHB Definition of a Right Artinian Ring - Cohn - page 66
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MHB Prove that the sum is equal to -1.
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MHB Free modules, M_n(R)-modules and M_N(R)-R-bimodules - Berrick and Keating
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MHB Infinite Direct Sums and Standard Inclusions and Projections
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MHB Direct Products and External Direct Sums
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Graduate Question about invariant w.r.t. a group action
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Undergrad Understanding Linear Algebra Solutions: Sketching and Ratios Explained
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Graduate Compensating for Accelerometer Misalignment
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MHB Determining if a set is a subspace.
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Undergrad What is is neither injective, surjective, and bijective?
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MHB Proof: $K[a]$ is a Field & if $K(a)=K[a]$, then $a$ is Algebraic Over $K$
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MHB What Determines Group Homomorphisms Between Rational Numbers?
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MHB Modules of Finite Length - Cohn, page 61
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MHB Generalizing Rigid Motions Group w/ Metric
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MHB What is the Definition of a Derivation for a Lie Algebra?
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Undergrad Proof of R being a Vector Space - Best Resources Available
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Graduate SU(2) as a normal subgroup of SL(2, C)
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MHB Definition of SO(n): O(n) & SL(n, \mathbb{R}) Intersection
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Graduate Writing 3rd Order Tensor Symmetric Part in Tensor Form
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Graduate Are All Indecomposable Groups Cyclic?
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Undergrad Is simultaneous row operation allowed in reducing a matrix to row echelon form?
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Graduate Why Does a Functional Depend on the Curve and Its Derivative?
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Undergrad Show that origin in R^n is the n-tuple 0=(0,0, .,0)
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MHB A group of even order contains an odd number of elements of order 2
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MHB Looking for an online Algebra resource
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MHB Subnormal Series and Composition Series
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MHB Theorem on the Lengths of Modules - Cohn, Theorem 2.5
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Graduate What are the algebra prerequisites for Lie groups?
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MHB Show that the elements have the same order
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MHB Verifying Sentences about Groups: Answers and Hints
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MHB Help Peter Prove Simple Proposition on Simple Groups & Maximal Normal Subgroups
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MHB Factor Groups and Simple Groups - Fraleigh: Theorem 15.18
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MHB Show that there are y,z such that y,z commute and their order is m and n
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MHB A cyclic group with only one generator can have at most two elements
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MHB Vector algebra- centroid of tetrahedron
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Graduate Solving Doubts When Showing Simple Properties of Norms
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MHB Proof that covariance matrix is positive semidefinite
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Undergrad Finding intersection of three planes
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Any1 can recommend any good e-book for linear algebra ?
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Graduate Possible title: When Does the Kernel of a Homomorphism Reduce to the Identity?
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Undergrad Solutions to Span of Functions Problems
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MHB Definitions of Algebras in Cohn and in Golan
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Graduate Symmetric Tensor Product in Pic. 1 - Explained
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MHB Solving Linear Transformations with Matrix A and Vectors u1 & u2
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