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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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 Free Groups - Dmmit & Fooote - Section 6.3
- 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 ·
Free Groups - Dummit & Fooote - Section 6.3
- 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 Error in Vector Addition: U & V Perpendicular
- 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: Showing Equality of Group G and G_a
- 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 ·
Proof: Every Subgroup of Cyclic $H$ is 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 Question about using matrices for differential equations
- 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 ·
Proving $\text{GL}_{2}(R): Showing Homomorphism & Isomorphism
- 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) | Cyclotomic Polynomials
- mathjam0990
- · Replies 4 ·
Math Problem: Rotation on z Axis
- Coal
- · Replies 3 ·
Principle Ideal in F[x] & Primitive nth root of unity
- mathjam0990
- · Replies 2 ·
Undergrad Basis of a Tensor Product - Theorem 10.2 - Another Question
- 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 ·
Understanding the Chinese Remainder Theorem for $\mathbb{Z}^{\times} _{20}$
- NoName3
- · Replies 5 ·
How many necklaces can we create?
- mathmari
- · Replies 44 ·
Linear Algebra: Analyzing A Linear Transformation
- 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 ·
Solving the Mystery of the Table: Explaining $g = (123)$
- 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 ·
Boost Your Cosine-Sine Isotherm Sketching Skills | Expert Tips & Guidance
- brunette15
- · Replies 2 ·
How to Determine the Order of \( g^8 \) in a Group?
- Guest2
- · Replies 3 ·
Undergrad Confused on 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 ·
Solve System of Equations: Unique Solution & Geometric Explanation
- Guest2
- · Replies 1 ·
Undergrad Vector Triple Product: Are a & c Parallel or Collinear?
- 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 ·
Field Extensions for polynomials
- mathjam0990
- · Replies 3 ·
Dual Vector Space and Dual Basis - another question - Winitzki Section 1-6
- Math Amateur
- · Replies 2 ·