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.
Threads
Splitting field and Galois group of x⁴−2x²+9 over ℚ
- mathjam0990
- · Replies 3 ·
P-Adic Localization in Rational Numbers: A Proof of Local Subring Property
- mathmari
- · Replies 1 ·
Undergrad When is a matrix diagonalizable in terms of geometric multiplicities?
- Bullington
- · Replies 5 ·
Is Every Non-Zero Element in a Finite Ring Invertible?
- mathmari
- · Replies 23 ·
Why Are Nilpotent Elements Significant in Ring Theory?
- mathmari
- · Replies 4 ·
Applying rotation matrix to make inclined plane flat again
- Maestroo
- · Replies 2 ·
Undergrad Why free groups have no relations satisfied by generators
- Math Amateur
- · Replies 8 ·
List the elements of the field F = F3[x] / < x2 + 1 >
- MupptMath
- · Replies 1 ·
Cooperstein Theorem 10.3 on tensor products and universality
- Math Amateur
- · Replies 1 ·
Why do free groups have no relations in F(S)?
- Math Amateur
- · Replies 2 ·
Graduate How to Solve the Inequality x^2 + 2ix + 3 < 0?
- Dacu
- · Replies 9 ·
What are some important properties of the Commutator Group of D_n?
- mathmari
- · Replies 7 ·
Linear Programming word problems
- glaceau
- · Replies 1 ·
Why Can't a Proper Normal Subgroup Contain a Sylow Normalizer in a Group?
- mathmari
- · Replies 1 ·
High School Why does W ^ V = U - W give (c, 0, a) = (1-a, -b, -c)?
- Amine_prince
- · Replies 4 ·
Undergrad A real matrix and its inverse share the same eigenvectors?
- Happiness
- · Replies 2 ·
Undergrad Sylow subgroup of some factor group
- moont14263
- · Replies 3 ·
Undergrad Tensor product existence proof in Cooperstein theorem 10.1
- Math Amateur
- · Replies 28 ·
Number of orbits of G on Ω×Ω equals orbits of G_a on Ω?
- mathmari
- · Replies 34 ·
Undergrad Properties of Tensor Products - Cooperstein, Theorem 10.3
- Math Amateur
- · Replies 5 ·
G contains a normal p-Sylow subgroup
- mathmari
- · Replies 5 ·
Describe the units of Z[sqrt 2]
- Math Amateur
- · Replies 15 ·
Undergrad Tensor Products - Issue with Cooperstein, Theorem 10.3
- Math Amateur
- · Replies 2 ·
Show that it is a normal subgroup of S4
- mathmari
- · Replies 27 ·
How can we find all the normal subgroups?
- mathmari
- · Replies 11 ·
Subgroups of a cyclic normal subgroup are normal in G
- mathmari
- · Replies 12 ·
Show that the group is not simple
- mathmari
- · Replies 5 ·
Undergrad True or False: A Linear System Must Have a Unique Solution
- Valour549
- · Replies 1 ·
High School Trying to understand function transformations
- pctopgs
- · Replies 7 ·
Graduate Eigenstates of "summed" matrix
- ilvreth
- · Replies 1 ·
Multiplicative group of matrices is nilpotent
- mathmari
- · Replies 25 ·
Undergrad Can you Explain this SVD Application?
- ecastro
- · Replies 8 ·
Undergrad Solving a 2×2 system of differential equations with eigenvalues
- EtherNohow
- · Replies 6 ·
What Are the Composition Series for \(A_4\) and \(S_3 \times \mathbb{Z}_2\)?
- mathmari
- · Replies 17 ·
Undergrad Transformation of Tensor Components
- FluidStu
- · Replies 2 ·
Is \(\pi\) Algebraic of Degree 3 Over Any Extension of \(\mathbb{Q}\)?
- Kiwi1
- · Replies 1 ·
Undergrad Basis of a Tensor Product - Cooperstein - Theorem 10.2
- Math Amateur
- · Replies 14 ·
Normal series and composition series
- mathmari
- · Replies 8 ·
Graduate Isomorphism between a linear space and its dual
- Geofleur
- · Replies 8 ·
Is Every Group of Order 135 Nilpotent?
- mathmari
- · Replies 14 ·
Graduate Fermat's Theorem: Proven by Euler and By Me?
- excogitator
- · Replies 1 ·
Undergrad What are the irreducible representations of point groups and how do I find them?
- Asteropaeus
- · Replies 6 ·
The group is isomorphic to one of the groups
- mathmari
- · Replies 9 ·
Show that each such group is solvable
- mathmari
- · Replies 13 ·
Inequality related to number of p-Sylow subgroups
- mathmari
- · Replies 2 ·
Graduate Artinian rings are noetherian, why does this make sense?
- PsychonautQQ
- · Replies 2 ·
Units in M₂(R) and homomorphisms to GL₂(R)
- NoName3
- · Replies 1 ·
Undergrad Conditions on negative definiteness
- p4wp4w
- · Replies 5 ·
Show that the intersection is a pp -Sylow subgroup
- mathmari
- · Replies 3 ·
Graduate Are Minimal Left Ideals in Hassani's Algebra Always Trivial?
- Geofleur
- · Replies 4 ·
How Do You Find the Multiplicative Inverse in \( Z_{360}[x] \)?
- corkycorey101
- · Replies 1 ·
Is \( f(P) \) a \( p \)-Sylow Subgroup of \( H \)?
- mathmari
- · Replies 3 ·
Prove Q(ζp) = Q(ζip) for p-th cyclotomic field
- mathjam0990
- · Replies 4 ·
Math Problem: Rotation on z Axis
- Coal
- · Replies 3 ·
Minimal polynomial of ζ + ζ⁻¹ where ζ is a primitive 5th root of unity
- mathjam0990
- · Replies 2 ·
Undergrad Tensor product basis in Cooperstein's Theorem 10.2
- Math Amateur
- · Replies 2 ·
Undergrad General solution to a linear equation is particular solution plus kernel
- Woolyabyss
- · Replies 2 ·
Proof of Existence of Tensor Product: Cooperstein Theorem 10.1
- Math Amateur
- · Replies 5 ·
Undergrad How do I convert [D]=[A][ B]T[C] to index notation?
- kezzstar
- · Replies 6 ·
Undergrad Why does Z have a universal mapping property in tensor product existence?
- Math Amateur
- · Replies 4 ·
How many necklaces can we create?
- mathmari
- · Replies 44 ·
Linear transformation part D2
- Zoey93
- · Replies 1 ·
Question from Jesse about Gaussian Elimination and LU factorisation.
- Prove It
- · Replies 1 ·
Undergrad Understanding Number Theory Proofs: Order of Elements in Finite Groups
- cragar
- · Replies 3 ·
Theorem 6.10 in Knapp's Basic Algebra: Exploring Bilinearity & Descending Maps
- Math Amateur
- · Replies 5 ·
Undergrad Understanding [T]_gamma and Its Purpose in Linear Transformations
- DhineshKumar
- · Replies 4 ·
Undergrad Tensor product theorem 6.10 in Knapp's Basic Algebra
- Math Amateur
- · Replies 3 ·
Undergrad Knapp's notation for direct sum in tensor product construction
- Math Amateur
- · Replies 3 ·
Tensor Product - Knapp, Chapter VI, Section 6
- Math Amateur
- · Replies 5 ·
Proving Equivalence of $g' \in Hg$, $g'g^{-1} \in H$, and $Hg = Hg'$
- NoName3
- · Replies 3 ·
Zero divisors preserved by ring isomorphisms
- corkscrew062
- · Replies 1 ·
Understanding Rings: Example of Homomorphism/Isomorphism
- corkycorey101
- · Replies 2 ·
How do you get g = (123) from the table?
- Guest2
- · Replies 3 ·
Can a group of order $2^6\cdot 5^6$ be simple?
- mathmari
- · Replies 23 ·
Find Left Cosets of Subgroup in $\mathbb{Z}_{15}, D_4$
- NoName3
- · Replies 4 ·
Proving Two Rings Are Isomorphic
- cs0978
- · Replies 1 ·
Sketching isotherms of cos(x)sinh(y)
- brunette15
- · Replies 2 ·
How to Determine the Order of \( g^8 \) in a Group?
- Guest2
- · Replies 3 ·
Undergrad Identity operator and the definition of projection
- JonnyG
- · Replies 3 ·
Undergrad Difference between 'Field' (algebra) and 'Field' (geometry)
- FluidStu
- · Replies 12 ·
Undergrad Aren't all linear operators one-to-one and onto?
- pellman
- · Replies 10 ·
Does Lemma 3 in Winitzki's Tensor Product Dimension Section Clarify Covectors?
- Math Amateur
- · Replies 13 ·
The Uniqueness of a Tensor Product
- Math Amateur
- · Replies 2 ·
The probability that two elements commute
- mathmari
- · Replies 7 ·
How can we prove the equality of orders for finite subgroups of a group?
- mathmari
- · Replies 8 ·
Decide h so that the linear system has infinite solutions
- mpdancow
- · Replies 1 ·
Undergrad Why only normal subgroup is used to obtain group quotient
- SVN
- · Replies 5 ·
Finding the Equation of a Plane Perpendicular to a Given Line
- brunette15
- · Replies 2 ·
Undergrad Calculating the number of real parameters of a unitary matri
- StuartY
- · Replies 6 ·
When does this 3x3 system have a unique solution?
- Guest2
- · Replies 1 ·
Undergrad Can parallel vectors satisfy the vector triple product equality?
- debjit625
- · Replies 1 ·
Undergrad How Does Covector Existence Relate to Tensor Dimensions in Winitzki's Lemma 3?
- Math Amateur
- · Replies 3 ·
Undergrad Coefficients of a vector regarded as a function of a vector
- Math Amateur
- · Replies 13 ·
Cartesian Equation of the Plane Passing Through Two Vectors
- Guest2
- · Replies 3 ·
Linear transformation and its matrix
- Guest2
- · Replies 8 ·
Proving $(T^2-I)(T-3I) = 0$ for Linear Operator $T$
- Guest2
- · Replies 4 ·
High School Is the Null Space of an Operator Defined by Its Zero Eigenvalue?
- maNoFchangE
- · Replies 4 ·
Is There a Solution for 6 Degree of Freedom Solid Body Movement Equations?
- Anton1
- · Replies 5 ·
Linear Subspaces: Properties and Examples
- Guest2
- · Replies 2 ·