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 Why is Q[x]/(x²-5) equal to Q[√5]?
- Math Amateur
- · Replies 15 ·
Undergrad Why must an isomorphism between 2Z and 3Z result in mu(2) = +/- 3?
- Mr Davis 97
- · Replies 7 ·
Why is Q[x]/(x² - 5) equal to Q[√5]?
- Math Amateur
- · Replies 2 ·
Graduate Galois theorem in general algebraic extensions
- coquelicot
- · Replies 6 ·
Undergrad How Do I Prove Polynomials Span P2?
- HenryFa
- · Replies 1 ·
Undergrad Does this theorem need that Ker{F}=0?
- jamalkoiyess
- · Replies 1 ·
Undergrad Why is p(x) irreducible if p(α)=0 in Lovett 7.1.10?
- Math Amateur
- · Replies 6 ·
High School Is the transpose of a singular matrix always singular?
- PrathameshR
- · Replies 1 ·
Undergrad Kronecker's Theorem - Anderson and Feil, Theorem 42.1
- Math Amateur
- · Replies 10 ·
Is the map F → F[x]/<p> in Kronecker's theorem surjective?
- Math Amateur
- · Replies 1 ·
Show this matrix is isomorphic to complex number
- Confusedalways
- · Replies 2 ·
Undergrad Finding x and y coordinates to graph 2x+3y=0
- Bobs
- · Replies 2 ·
Undergrad Linear transformation of a given coordinate
- kidsasd987
- · Replies 1 ·
Undergrad Have These Hypercomplex Numbers Already Been Discovered?
- puzzled fish
- · Replies 14 ·
Graduate From Lie algebras to Dynkin diagrams and back again
- tom.stoer
- · Replies 2 ·
Undergrad Non-negativity of the inner product
- Mr Davis 97
- · Replies 27 ·
Prime subfields and divisions in Lovett's Proposition 7.1.3
- Math Amateur
- · Replies 5 ·
Undergrad Proving a set is linearly independant
- cathal84
- · Replies 5 ·
Undergrad Prime subfield of characteristic p equals Z/pZ in Lovett 7.1.3
- Math Amateur
- · Replies 4 ·
Undergrad Lovett vs Dummit-Foote notation for F[α] and F(α)
- Math Amateur
- · Replies 12 ·
Graduate Has anyone read Ken Conrow's Collatz Conjecture website?
- Mensanator
- · Replies 2 ·
Why does irreducibility of 2 imply associates in Z[√-5]?
- Math Amateur
- · Replies 2 ·
Undergrad Distinctiveness of the set of nxn matrices as a ring
- Mr Davis 97
- · Replies 5 ·
Undergrad Why irreducibility of 2 implies α is associate to 1 or 2
- Math Amateur
- · Replies 6 ·
Show Equivalence: $a^d \equiv 1 \pmod n$
- evinda
- · Replies 3 ·
Undergrad Hermitian operators, matrices and basis
- Trixie Mattel
- · Replies 5 ·
Quadratic Polynomials and Irreducibles and Primes
- Math Amateur
- · Replies 2 ·
High School Why Didn't the Eigenvector Approach Work for This Matrix?
- jonjacson
- · Replies 9 ·
How to find diagonal matrix D without calculating P inverse
- tomc612
- · Replies 2 ·
Undergrad How to find angle between vectors from dot and cross product
- andylatham82
- · Replies 9 ·
Undergrad Theorem 1.2.2 on irreducibility in Alaca and Williams
- Math Amateur
- · Replies 5 ·
Undergrad Proving a property when elements of a group commute
- Mr Davis 97
- · Replies 6 ·
Undergrad First Isomorphism Theorem and rings of fractions in Lovett 6.2.6
- Math Amateur
- · Replies 8 ·
Graduate Is My Transformation Matrix Correct?
- kajalschopra
- · Replies 3 ·
Field extension basis: expressing products in terms of basis elements
- Math Amateur
- · Replies 4 ·
Undergrad Field extension basis multiplication in Ireland and Rosen Ch 12
- Math Amateur
- · Replies 2 ·
First Isomorphism Theorem in Lovett Proposition 6.2.6
- Math Amateur
- · Replies 2 ·
Undergrad What is the group action of G on itself by left conjugation?
- Mr Davis 97
- · Replies 1 ·
Undergrad Proving an exponent law in group theory
- Mr Davis 97
- · Replies 5 ·
Undergrad Definition of an irreducible element in an integral domain
- Math Amateur
- · Replies 84 ·
Undergrad Permutation group and character table
- Konte
- · Replies 6 ·
Proving a Vector in $\Bbb R^2$ is of the Form $au+bv$
- Niamh1
- · Replies 2 ·
Undergrad Rings of fractions isomorphic to rationals in Lovett 6.2.4
- Math Amateur
- · Replies 3 ·
High School Complex numbers satisfying |z+1| = |z+i| and |z| = 5
- matrixone
- · Replies 5 ·
Undergrad Can an Abelian Group Be Isomorphic to a Non-Abelian Group in Physics?
- Konte
- · Replies 6 ·
Undergrad Determining Vector Direction: Finding Unit Vectors
- Gurasees
- · Replies 2 ·
Can I Use the Difference of Cubes Formula for Factoring 27 - (a - b)^3?
- mathdad
- · Replies 5 ·
Undergrad Proving a lemma on decomposition of V to T-cyclic subspace
- Adgorn
- · Replies 1 ·
Undergrad ##SU(2)## generators in ##1##, ##2## and ##3## dimensions
- spaghetti3451
- · Replies 5 ·
Prove that the paraboloids have a common tangent planes
- debrajr
- · Replies 1 ·
Is a^2 - 6a + 12 Irreducible Over the Integers?
- mathdad
- · Replies 2 ·
Show that Z2 × Z3 is isomorphic to the group G = {1,2,4,8,10}
- rss1
- · Replies 7 ·
Undergrad Trigonometric series with normalised coefficients
- Gaetano F
- · Replies 2 ·
Undergrad A new vector-product for geometric algebra?
- N88
- · Replies 1 ·
Ring of fractions isomorphic to ℚ in Lovett 6.2.4
- Math Amateur
- · Replies 2 ·
Undergrad Understanding "Hat e" Notation
- iDimension
- · Replies 4 ·
Undergrad How is Conjugacy a Group Action?
- Mr Davis 97
- · Replies 4 ·
How do you nondimensionalize an equation with substituted variables?
- jessicamorgan
- · Replies 4 ·
Calculate Cosine of a Matrix: Solutions to Systems
- jessicamorgan
- · Replies 3 ·
Undergrad Understanding Co-vectors to Dual Spaces and Linear Functionals
- JuanC97
- · Replies 6 ·
Proving K is a Subgroup of G: Subgroup Nesting in H and L
- Jen917
- · Replies 3 ·
High School Certainty of being able to solve linear equation
- Mr Davis 97
- · Replies 4 ·
Proving N(H) is a Subgroup of G Containing H
- Jen917
- · Replies 1 ·
Ring homomorphisms from Z to Z are only zero and identity
- Math Amateur
- · Replies 2 ·
Markov Chains - Finding a Transition Matrix for Probabilities
- Umar
- · Replies 5 ·
High School Why is \( (1 + \sqrt{-5}) \times (1 - \sqrt{-5}) \) Equal to 6?
- harrylentil
- · Replies 7 ·
Undergrad Regarding the linear dependence of eigenvectors
- Adgorn
- · Replies 2 ·
Graduate Find vectors in Orthogonal basis set spanning R4
- Minal
- · Replies 2 ·
Undergrad Fermat's Little Theorem proof: multiplicative cancellation in fields
- Math Amateur
- · Replies 3 ·
Undergrad What is the Basis for the Null Space in Matrix A?
- Lord Anoobis
- · Replies 6 ·
High School Find the Minimum Value of Expression Involving Positive Real Numbers
- matrixone
- · Replies 2 ·
Fermat's Little Theorem proof in Anderson and Feil 8.7
- Math Amateur
- · Replies 2 ·
Why m > r and s > 1 in Anderson and Feil theorem 8.6
- Math Amateur
- · Replies 2 ·
Undergrad Units in Z_m have gcd(x,m)=1 in theorem 8.6
- Math Amateur
- · Replies 5 ·
Undergrad Proving a result about invertibility without determinants
- Mr Davis 97
- · Replies 2 ·
Undergrad DimKer(T) = 0 <--> T is injective
- Mr Davis 97
- · Replies 6 ·
Graduate Difference Between Outer and Tensor
- devd
- · Replies 1 ·
Undergrad Trying to understand least squares estimates
- Nastya
- · Replies 3 ·
Linear Algebra Conditions: Solving for ab≠1
- Terry_Destefano
- · Replies 3 ·
Undergrad Express power sums in terms of elementary symmetric function
- Yiming Xu
- · Replies 1 ·
Why is Z[1/2] equal to {k/2^n | k,n ∈ Z}?
- Math Amateur
- · Replies 5 ·
Undergrad The proof of the above theorem is similar to the proof of the above statement.
- Mr Davis 97
- · Replies 4 ·
Undergrad Generalizing the definition of a subgroup
- Mr Davis 97
- · Replies 1 ·
Undergrad For groups, showing that a subset is closed under operation
- Mr Davis 97
- · Replies 1 ·
Undergrad Entries in a direction cosine matrix as derivatives
- maxhersch
- · Replies 1 ·
Factoring 6t^2+17t+7 by grouping
- hououin kyouma1
- · Replies 2 ·
Undergrad Can Least Squares Solve for Rigid Transform?
- PabloBot
- · Replies 3 ·
Understanding Irreducible Elements in Integral Domains - Peter's Questions
- Math Amateur
- · Replies 1 ·
Undergrad When is D_{n} abelian? What's wrong with the proof?
- AdamsJoK
- · Replies 2 ·
Undergrad Change of Basis and Unitary Transformations
- devd
- · Replies 5 ·
Undergrad Why is Z[1/2] the smallest subring containing Z and 1/2?
- Math Amateur
- · Replies 2 ·
Undergrad What Are the Practical Applications of Matrix Division?
- Sledge
- · Replies 2 ·
Finding the Linear Equation Relating Price and Number of Widgets Sold
- woof123
- · Replies 2 ·
Undergrad Why must units satisfy ab = ba = 1 in noncommutative rings?
- Math Amateur
- · Replies 8 ·
Undergrad Linear Algebra Conditions: Solving for ab ≠ 1
- Terry_Destefano
- · Replies 1 ·
Graduate Can commuting matrices have different eigenvectors?
- LagrangeEuler
- · Replies 7 ·
Undergrad Verifying a linear transformation
- Mr Davis 97
- · Replies 2 ·
Find value of x and area of parallelogram: a,b,c,P
- Niamh1
- · Replies 2 ·
Why must both ab and ba equal 1 for a to be a unit?
- Math Amateur
- · Replies 2 ·
Induction to find the determinant
- mathmari
- · Replies 2 ·