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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 Kronecker's Theorem - Anderson and Feil, Theorem 42.1, Chapter 42 .... ....
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MHB Show this matrix is isomorphic to complex number
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Undergrad Solve 2x+3y=0: Find x & y Points for Line
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Undergrad Linear transformation of a given coordinate
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Undergrad Have These Hypercomplex Numbers Already Been Discovered?
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Graduate From Lie algebras to Dynkin diagrams and back again
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Undergrad Non-negativity of the inner product
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MHB Prime Subfiellds - Lovett, Proposition 7.1.3 ....
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Undergrad Proving a set is linearly independant
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Undergrad Prime Subfiellds - Lovett, Proposition 7.1.3 ....
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Undergrad Basic Notation for Field Extensions ....
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Graduate Has anyone read Ken Conrow's Collatz Conjecture website?
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MHB Irreducibles and Primes in Integral Domains ....
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Undergrad Distinctiveness of the set of nxn matrices as a ring
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Undergrad Irreducibles and Primes in Integral Domains ....
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MHB Show Equivalence: $a^d \equiv 1 \pmod n$
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Undergrad Hermitian operators, matrices and basis
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MHB Quadratic Polynomials and Irreducibles and Primes
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High School Why Didn't the Eigenvector Approach Work for This Matrix?
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MHB Finding Matrix D Without Calculating P Inverse: Help Appreciated!
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Undergrad How to find angle between vectors from dot and cross product
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Undergrad Quadratic Polynomials and Irreducibles and Primes ....
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Undergrad Proving a property when elements of a group commute
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Undergrad Rings of Fractions .... Lovett, Section 6.2, Proposition 6.2
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Graduate Is My Transformation Matrix Correct?
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MHB Basics of Field Extensions .... .... Ireland and Rosen, Ch 12
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Undergrad Basics of Field Extensions .... .... Ireland and Rosen, Ch 12
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MHB Rings of Fractions .... Lovett, Section 6.2, Proposition 6.2.6 .... ....
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Undergrad What is the group action of G on itself by left conjugation?
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Undergrad Proving an exponent law in group theory
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Undergrad Definition of an irreducible element in an integral domain
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Undergrad Permutation group and character table
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MHB Proving a Vector in $\Bbb R^2$ is of the Form $au+bv$
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Undergrad Rings of Fractions .... Lovett, Section 6.2 ....
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High School Complex Number Solutions for |z+1| = |z+i| and |z| = 5
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Undergrad Can an Abelian Group Be Isomorphic to a Non-Abelian Group in Physics?
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Undergrad Determining Vector Direction: Finding Unit Vectors
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MHB Can I Use the Difference of Cubes Formula for Factoring 27 - (a - b)^3?
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Undergrad Proving a lemma on decomposition of V to T-cyclic subspace
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Undergrad ##SU(2)## generators in ##1##, ##2## and ##3## dimensions
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MHB Prove that the paraboloids have a common tangent planes
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MHB Is a^2 - 6a + 12 Irreducible Over the Integers?
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MHB Isomorphic Groups: Z2 X Z3 & G = (1,2,4,8,10)
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Undergrad Trigonometric series with normalised coefficients
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Undergrad A new vector-product for geometric algebra?
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MHB Rings of Fractions .... Lovett, Section 6.2 ....
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Undergrad Understanding "Hat e" Notation
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Undergrad How is Conjugacy a Group Action?
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MHB How do you nondimensionalize an equation with substituted variables?
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MHB Calculate Cosine of a Matrix: Solutions to Systems
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Undergrad Understanding Co-vectors to Dual Spaces and Linear Functionals
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MHB Proving K is a Subgroup of G: Subgroup Nesting in H and L
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High School Certainty of being able to solve linear equation
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MHB Proving N(H) is a Subgroup of G Containing H
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MHB Ring Homomorphisms from Z to Z .... Lovett, Ex. 1, Section 5.4 .... ....
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MHB Markov Chains - Finding a Transition Matrix for Probabilities
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High School Why is \( (1 + \sqrt{-5}) \times (1 - \sqrt{-5}) \) Equal to 6?
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Undergrad Regarding the linear dependence of eigenvectors
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Graduate Find vectors in Orthogonal basis set spanning R4
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Undergrad Fermat's Little Theorem .... Anderson and Feil, Theorem 8.7 .
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Undergrad What is the Basis for the Null Space in Matrix A?
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High School Find the Minimum Value of Expression Involving Positive Real Numbers
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MHB Fermat's Little Theorem .... Anderson and Feil, Theorem 8.7 .... ....
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MHB Units in Z_m .... Anderson and Feil, Theorem 8.6 .... ....
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Undergrad Units in Z_m .... Anderson and Feil, Theorem 8.6 .... ....
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Undergrad Proving a result about invertibility without determinants
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Undergrad DimKer(T) = 0 <--> T is injective
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Graduate Difference Between Outer and Tensor
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Undergrad Trying to understand least squares estimates
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MHB Linear Algebra Conditions: Solving for ab≠1
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Undergrad Express power sums in terms of elementary symmetric function
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MHB Rings Generated by Elements - Lovett, Example 5.2.1 .... ....
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Undergrad The proof of the above theorem is similar to the proof of the above statement.
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Undergrad Generalizing the definition of a subgroup
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Undergrad For groups, showing that a subset is closed under operation
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Undergrad Entries in a direction cosine matrix as derivatives
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MHB Need help factoring and understanding Grouping
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Undergrad Can Least Squares Solve for Rigid Transform?
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MHB Understanding Irreducible Elements in Integral Domains - Peter's Questions
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Undergrad When is D_{n} abelian? What's wrong with the proof?
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Undergrad Change of Basis and Unitary Transformations
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Undergrad Rings Generated by Elements - Lovett, Example 5.2.1 .... ....
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Undergrad What Are the Practical Applications of Matrix Division?
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MHB Finding the Linear Equation Relating Price and Number of Widgets Sold
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Undergrad Thinking about the Definition of a Unit of a ring R .... ....
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Undergrad Linear Algebra Conditions: Solving for ab ≠ 1
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Graduate Matrices commute & Eigenvectors question
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Undergrad Verifying a linear transformation
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MHB Find value of x and area of parallelogram: a,b,c,P
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MHB Thinking about the Definition of a Unit of a ring R .... ....
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MHB Induction to find the determinant
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Undergrad Angle between two vectors with many dimensions
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Undergrad Simple Modules and Right Annihilator Ideals ....
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Undergrad Did Artin make a mistake regarding isomorphisms?
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Undergrad Solving a system of equation with matrices
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Undergrad Simple Modules and Maximal Right Ideals ....
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Undergrad Jacobson Radical and Right Annihilator Ideals ....
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MHB Exploring Proposition 6.1.7 and its Proof in Bland's "Rings and Their Modules"
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Undergrad Prove that V is the internal direct sum of two subspaces
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Undergrad How can I find the orthogonal matrix that diagonalises a given matrix?
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