Linear and Abstract Algebra Forum

Post thread
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.
MHB Proving a Vector in $\Bbb R^2$ is of the Form $au+bv$
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Rings of Fractions .... Lovett, Section 6.2 ....
  • · Replies 3 ·
Replies
3
Views
2K
High School Complex Number Solutions for |z+1| = |z+i| and |z| = 5
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Can an Abelian Group Be Isomorphic to a Non-Abelian Group in Physics?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Proving a lemma on decomposition of V to T-cyclic subspace
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad ##SU(2)## generators in ##1##, ##2## and ##3## dimensions
  • · Replies 5 ·
Replies
5
Views
2K
MHB Prove that the paraboloids have a common tangent planes
  • · Replies 1 ·
Replies
1
Views
2K
MHB Isomorphic Groups: Z2 X Z3 & G = (1,2,4,8,10)
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Trigonometric series with normalised coefficients
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad A new vector-product for geometric algebra?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Rings of Fractions .... Lovett, Section 6.2 ....
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How is Conjugacy a Group Action?
  • · Replies 4 ·
Replies
4
Views
2K
MHB How do you nondimensionalize an equation with substituted variables?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Calculate Cosine of a Matrix: Solutions to Systems
  • · Replies 3 ·
Replies
3
Views
2K
MHB Proving K is a Subgroup of G: Subgroup Nesting in H and L
  • · Replies 3 ·
Replies
3
Views
2K
MHB Proving N(H) is a Subgroup of G Containing H
  • · Replies 1 ·
Replies
1
Views
2K
MHB Ring Homomorphisms from Z to Z .... Lovett, Ex. 1, Section 5.4 .... ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Markov Chains - Finding a Transition Matrix for Probabilities
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Regarding the linear dependence of eigenvectors
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Find vectors in Orthogonal basis set spanning R4
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Fermat's Little Theorem .... Anderson and Feil, Theorem 8.7 .
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad What is the Basis for the Null Space in Matrix A?
  • · Replies 6 ·
Replies
6
Views
3K
High School Find the Minimum Value of Expression Involving Positive Real Numbers
  • · Replies 2 ·
Replies
2
Views
2K
MHB Fermat's Little Theorem .... Anderson and Feil, Theorem 8.7 .... ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Units in Z_m .... Anderson and Feil, Theorem 8.6 .... ....
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Units in Z_m .... Anderson and Feil, Theorem 8.6 .... ....
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Proving a result about invertibility without determinants
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad DimKer(T) = 0 <--> T is injective
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Difference Between Outer and Tensor
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Trying to understand least squares estimates
  • · Replies 3 ·
Replies
3
Views
1K
MHB Linear Algebra Conditions: Solving for ab≠1
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Express power sums in terms of elementary symmetric function
  • · Replies 1 ·
Replies
1
Views
2K
MHB Rings Generated by Elements - Lovett, Example 5.2.1 .... ....
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad The proof of the above theorem is similar to the proof of the above statement.
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Generalizing the definition of a subgroup
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad For groups, showing that a subset is closed under operation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Entries in a direction cosine matrix as derivatives
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Can Least Squares Solve for Rigid Transform?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Understanding Irreducible Elements in Integral Domains - Peter's Questions
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad When is D_{n} abelian? What's wrong with the proof?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Change of Basis and Unitary Transformations
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Rings Generated by Elements - Lovett, Example 5.2.1 .... ....
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Thinking about the Definition of a Unit of a ring R .... ....
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Linear Algebra Conditions: Solving for ab ≠ 1
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Matrices commute & Eigenvectors question
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Verifying a linear transformation
  • · Replies 2 ·
Replies
2
Views
1K
MHB Thinking about the Definition of a Unit of a ring R .... ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Induction to find the determinant
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Angle between two vectors with many dimensions
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad Simple Modules and Right Annihilator Ideals ....
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Did Artin make a mistake regarding isomorphisms?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Solving a system of equation with matrices
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Simple Modules and Maximal Right Ideals ....
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Jacobson Radical and Right Annihilator Ideals ....
  • · Replies 1 ·
Replies
1
Views
2K
MHB Exploring Proposition 6.1.7 and its Proof in Bland's "Rings and Their Modules"
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Prove that V is the internal direct sum of two subspaces
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad How can I find the orthogonal matrix that diagonalises a given matrix?
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad What is the concept of tensor product and how is it used in mathematics?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Understanding Vector Spaces with functions
  • · Replies 24 ·
Replies
24
Views
4K
Graduate Isomorphism concepts,( example periods elliptic functions )
  • · Replies 8 ·
Replies
8
Views
2K
Can Hermitian Matrices be Traceless?
  • · Replies 7 ·
Replies
7
Views
8K
MHB Proof of Bland's Example 13: Simple Modules and Quotients of Maximal Modules
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Simple Modules and quotients of maximal modules, Bland Ex 13
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Kronecker product recovering the initial representation?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Matrices and linear transformations. Where did I go wrong?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Vector Space: Scalar Restriction in ℤ2
  • · Replies 2 ·
Replies
2
Views
1K
MHB Calculating Determinants of Matrices: A How-To Guide
  • · Replies 5 ·
Replies
5
Views
2K
High School Group of Symmetry of Rectangle: Reflections & Diagonals
  • · Replies 8 ·
Replies
8
Views
1K
Undergrad Existence of spanning set for every vector space
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Commutative diagrams and equality of composition
  • · Replies 1 ·
Replies
1
Views
1K
MHB Proving Equivalence of Statements Involving Endomorphisms - Can We Take $v=x$?
  • · Replies 10 ·
Replies
10
Views
3K
MHB Is the transformation matrix of $\Phi$ in relation to $B$ correct?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Is Group Operation in (G,*) Considered Composition in Mathematics?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Is a symmetric matrix with positive eigenvalues always real?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Terminology for Substructures in Vector Spaces
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Are Splitting Fields Unique for Different Polynomial Families?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Jacobson Radical and Direct Sums - Bland, Proposition 6.1.4
  • · Replies 3 ·
Replies
3
Views
2K
MHB Jacobson Radical and Direct Sums - Bland, Proposition 6.1.4 ....
  • · Replies 4 ·
Replies
4
Views
2K
MHB Does \(B\) Span Algebraically \(E\) Over \(F\)?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Exponent of Group Hey! :o - Answers to Questions
  • · Replies 16 ·
Replies
16
Views
4K
MHB It is an algebraically dependent set over F
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Understanding Separable Vector Spaces: The Basics Explained
  • · Replies 9 ·
Replies
9
Views
3K
MHB Field extensions and Galois goup
  • · Replies 2 ·
Replies
2
Views
2K
MHB Diagonalizable Matrix: How to Approach?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Definition of discrete Subgroup quick q
  • · Replies 10 ·
Replies
10
Views
2K
MHB Is $\Phi|_{U_2}$ a Vector Space Isomorphism?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Injective linear mapping - image
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Proving an inverse of a groupoid is unique
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Real parameters and imaginary generators
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Using determinant to find constraints on equation
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Basis of a Subspace of a Vector Space
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Linear algebra ( symmetric matrix)
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Question regarding root of Bring quintic not expressible with radicals
  • · Replies 37 ·
2
Replies
37
Views
6K
MHB Solving Linear Mapping Problems with Matrix $M$ in $\mathbb K^2$
  • · Replies 10 ·
Replies
10
Views
3K
MHB Pointwise and uniform convergence
  • · Replies 5 ·
Replies
5
Views
2K
MHB Solving for Invertible Matrix: What Am I Doing Wrong?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Why Does the Matrix Calculation Not Match Expected Results in Linear Mapping?
  • · Replies 1 ·
Replies
1
Views
2K
MHB What is the Intuition Behind Integral Over in Commutative Algebra?
  • · Replies 2 ·
Replies
2
Views
2K
MHB How do I draw the contour line and gradient of a function at a specific point?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Jacobson Radical and Rad(M) - Bland Corollary 6.1.3 ....
  • · Replies 10 ·
Replies
10
Views
2K