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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.
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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Graduate Transform 10 to 1000 Points on x^9 to x^2 Polynomial
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