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.
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Modules - Northott: Proposition 1
- Math Amateur
- · Replies 2 ·
Show that it satisfies the equation
- mathmari
- · Replies 12 ·
Show $\|.\|$ is an Norm: Prove Triangle Inequality
- Julio1
- · Replies 5 ·
Graduate Factor Groups: What am I thinking about wrongly here?
- PsychonautQQ
- · Replies 3 ·
Algebraic Proofs and Verifying identities
- abbarajum
- · Replies 5 ·
Graduate Is Matrix Addition Commutative?
- albega
- · Replies 4 ·
High School Modulus & Division: Last Digit of Numbers Explained
- Rishav sapahi
- · Replies 3 ·
Can every subring of an algebraic extension be a field?
- mathmari
- · Replies 8 ·
Graduate How do I make a change of basis with tensors in multilinear algebra?
- space-time
- · Replies 1 ·
Graduate Iterations of functions of noncommutative variables
- hilbert2
- · Replies 3 ·
Dimension and Basis of a Relation in R5
- Logan Land
- · Replies 6 ·
Find the coordinates of the expression
- Logan Land
- · Replies 4 ·
Find coordinates of f′, f′′, f′′′ in the basis
- Logan Land
- · Replies 20 ·
Showing Linearity of $\varphi$ for $K(a)$
- mathmari
- · Replies 5 ·
Can a Group Have a Trivial Automorphism Group with Less than Three Elements?
- Euge
- · Replies 5 ·
What Is the Splitting Field for \(x^{p^{80}}-1\) Over \(\mathbb{F}_p\)?
- mathmari
- · Replies 6 ·
Field extensions and degree of odd prime numbers
- mathmari
- · Replies 6 ·
Undergrad Why equating two planes does not provide solutions?
- MathewsMD
- · Replies 8 ·
Graduate Artin - domains don't seem to match
- Whovian
- · Replies 1 ·
Graduate Eigenstuff of Second Derivative
- Hertz
- · Replies 4 ·
Graduate Pfaffian and determinants of skew symmetric matrices
- camilus
- · Replies 1 ·
Undergrad Line operations on matrix products
- gummz
- · Replies 1 ·
Undergrad Defining a vector in magnitude,angle form.
- Hijaz Aslam
- · Replies 1 ·
Graduate Are the Functions Linearly Independent Based on the Matrix of Their Outputs?
- Alban1806
- · Replies 2 ·
Undergrad Line of intersection of two planes
- MarcL
- · Replies 2 ·
High School Finding determinant through Gaussian elimination
- purplecows
- · Replies 3 ·
Graduate Solving the Inversion Problem with RGB Filters
- Edward Zhang
- · Replies 1 ·
Graduate Is the Klein Four Group Identical to the Dihedral Group D2?
- ChrisVer
- · Replies 3 ·
How can I prove that $\theta_p$ is a p-Norm?
- evinda
- · Replies 7 ·
Graduate Associativity of Hadamard and matrix product
- Zoli
- · Replies 2 ·
Graduate Length-Norm inequality to root-n times Length (using 2|uv| <= |u|^2 + |v|^2)
- Sravoff
- · Replies 4 ·
Undergrad Why is det(C)=det(A)^(n-1) for cofactors and determinants?
- Unusualskill
- · Replies 1 ·
Let F ={0 , 1 , a , b} be a field with four elements.
- rayne1
- · Replies 2 ·
Undergrad Proving Non-Trivial Solutions of Ax = b
- HaLAA
- · Replies 3 ·
Units of the set of all Eisenstein Integers
- Math Amateur
- · Replies 6 ·
Ring of integer p-adic numbers.
- evinda
- · Replies 1 ·
Undergrad Proving Determinant of Matrix Unchanged by Adding Columns
- Unusualskill
- · Replies 2 ·
Show that Q adjoin square roots of 2, 3 is a vector space of dimension 4 over Q
- Ragnarok7
- · Replies 1 ·
Graduate Groups of homomorphisms of abelian groups
- JD_Shadowplay
- · Replies 1 ·
Showing that $A$ is an Ideal of $\mathbb{Q}[x]$ and Expressing it as $<f(x)>$
- mathmari
- · Replies 4 ·
Units of the Gaussian Integers, Z[i]
- Math Amateur
- · Replies 5 ·
Graduate Is intuition more important than logical proof in mathematics?
- hideelo
- · Replies 7 ·
Graduate Can you explain the determinant formula using permutation notation?
- Unusualskill
- · Replies 3 ·
Every submodule has at least one set of generators?
- Math Amateur
- · Replies 7 ·
Graduate Does the inverse of this special matrix have a power series expansion?
- srz
- · Replies 5 ·
Graduate Is the Canonical Basis in Mathematics Just a Useful Convention?
- rkaminski
- · Replies 6 ·
Graduate Properties of Kernels of Homeomorphisms
- WWGD
- · Replies 7 ·
What is the Proof for the Nonempty Intersection of Submodules Being a Submodule?
- Math Amateur
- · Replies 4 ·
Why must the ring $K[x]$ have infinitely many irreducible polynomials?
- mathmari
- · Replies 7 ·
Undergrad Transform Cylindrical coordinates into Cartesian Coordiantes
- kexanie
- · Replies 3 ·
The polynomial is irreducible iff the condition is satisfied
- mathmari
- · Replies 3 ·
Graduate Explicit construction of isomorphisms of low-rank Lie algebras.
- lpetrich
- · Replies 2 ·
Problem Regarding Left Unital Artinian Ring (set by Euge)
- Math Amateur
- · Replies 3 ·
Field extension-degree of the minimal polynom
- mathmari
- · Replies 1 ·
Ordered Index Sets for Direct Sums & Products of Modules: Explained by B&K
- Math Amateur
- · Replies 7 ·
Prove that the order of 5 modulo 2^k is 2^(k-2)
- Fermat1
- · Replies 8 ·
Direct Sums of Copies of Modules - B&K - Exercise 2.1.6 (iii)
- Math Amateur
- · Replies 7 ·
Show the Units of Zn with modular multiplication are a group
- E01
- · Replies 2 ·
Finding Notation for Left Invariant Vector Fields on Lie Groups
- topsquark
- · Replies 3 ·
Graduate Function scales eigenvalues, but what happens to eigenvectors?
- johnpjust
- · Replies 7 ·
Undergrad Finding Inverse of Matrix by using Gaussian-Jordan Elimination
- shuiki0306
- · Replies 6 ·
Definition of a Right Artinian Ring - Cohn - page 66
- Math Amateur
- · Replies 15 ·
Prove that the sum is equal to -1.
- evinda
- · Replies 7 ·
Free modules, M_n(R)-modules and M_N(R)-R-bimodules - Berrick and Keating
- Math Amateur
- · Replies 1 ·
Infinite Direct Sums and Standard Inclusions and Projections
- Math Amateur
- · Replies 1 ·
Direct Products and External Direct Sums
- Math Amateur
- · Replies 2 ·
Graduate Question about invariant w.r.t. a group action
- mnb96
- · Replies 3 ·
Undergrad Understanding Linear Algebra Solutions: Sketching and Ratios Explained
- woundedtiger4
- · Replies 3 ·
Graduate Compensating for Accelerometer Misalignment
- IMK
- · Replies 1 ·
Determining if a set is a subspace.
- AngrySnorlax
- · Replies 4 ·
Undergrad What is is neither injective, surjective, and bijective?
- woundedtiger4
- · Replies 9 ·
Proof: $K[a]$ is a Field & if $K(a)=K[a]$, then $a$ is Algebraic Over $K$
- mathmari
- · Replies 2 ·
What Determines Group Homomorphisms Between Rational Numbers?
- Fermat1
- · Replies 5 ·
Modules of Finite Length - Cohn, page 61
- Math Amateur
- · Replies 34 ·
Generalizing Rigid Motions Group w/ Metric
- topsquark
- · Replies 3 ·
What is the Definition of a Derivation for a Lie Algebra?
- topsquark
- · Replies 4 ·
Undergrad Proof of R being a Vector Space - Best Resources Available
- woundedtiger4
- · Replies 7 ·
Graduate SU(2) as a normal subgroup of SL(2, C)
- TrickyDicky
- · Replies 3 ·
Definition of SO(n): O(n) & SL(n, \mathbb{R}) Intersection
- topsquark
- · Replies 1 ·
Graduate Writing 3rd Order Tensor Symmetric Part in Tensor Form
- mikeeey
- · Replies 5 ·
Graduate Are All Indecomposable Groups Cyclic?
- metapuff
- · Replies 4 ·
Undergrad Is simultaneous row operation allowed in reducing a matrix to row echelon form?
- MathewsMD
- · Replies 5 ·
Graduate Why Does a Functional Depend on the Curve and Its Derivative?
- "Don't panic!"
- · Replies 1 ·
Undergrad Show that origin in R^n is the n-tuple 0=(0,0, .,0)
- woundedtiger4
- · Replies 6 ·
A group of even order contains an odd number of elements of order 2
- mathmari
- · Replies 3 ·
Looking for an online Algebra resource
- topsquark
- · Replies 6 ·
Subnormal Series and Composition Series
- Math Amateur
- · Replies 6 ·
Theorem on the Lengths of Modules - Cohn, Theorem 2.5
- Math Amateur
- · Replies 1 ·
Graduate What are the algebra prerequisites for Lie groups?
- kostas230
- · Replies 24 ·
Show that the elements have the same order
- mathmari
- · Replies 5 ·
Verifying Sentences about Groups: Answers and Hints
- mathmari
- · Replies 6 ·
Help Peter Prove Simple Proposition on Simple Groups & Maximal Normal Subgroups
- Math Amateur
- · Replies 3 ·
Factor Groups and Simple Groups - Fraleigh: Theorem 15.18
- Math Amateur
- · Replies 1 ·
Show that there are y,z such that y,z commute and their order is m and n
- mathmari
- · Replies 2 ·
A cyclic group with only one generator can have at most two elements
- mathmari
- · Replies 4 ·
Vector algebra- centroid of tetrahedron
- mathisfun1
- · Replies 3 ·
Graduate Solving Doubts When Showing Simple Properties of Norms
- dumb_curiosity
- · Replies 7 ·
Proof that covariance matrix is positive semidefinite
- AlanTuring
- · Replies 1 ·
Undergrad Finding intersection of three planes
- Tarrius
- · Replies 5 ·
Any1 can recommend any good e-book for linear algebra ?
- Unusualskill
- · Replies 5 ·