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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 How Do Planes Intersect in Various Linear Systems?
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Undergrad Splitting Fields: Anderson and Feil, Theorem 45.5 ....
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MHB Galois Theory - Fixed Field of F and Definition of Aut(K/F) ....
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MHB Splitting Fields: Anderson and Feil, Theorem 45.4
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Undergrad Splitting Fields: Anderson and Feil, Theorem 45.4 ....
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Undergrad Galois Theory - Fixed Field of F and Definition of Aut(K/F)
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Undergrad Galois Theory - Fixed Subfield of K by H ....
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MHB Galois Theory - Fixed Subfield of K by H ....
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MHB Galois Theory: Textbook recommendations?
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Undergrad Galois Theory - Structure Within Aut(K/Q) ....
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High School Associativity of Matrix multiplication
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MHB Automorphisms of Field Extensions .... Lovett, Example 11.1.8 .... ....
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Undergrad Automorphisms of Field Extensions .... Lovett, Example 11.1.8
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Undergrad Developing Intuition Behind Affine Subspaces: A Sample Problem
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High School Why does every subfield of Complex number have a copy of Q?
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High School Vector Space over Field of Real Numbers
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High School ##AB = I \implies BA = I##, for square matricies ##A,B##
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MHB Nested Matrix Elements: Define \Gamma^{\dagger}?
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Undergrad Intuition behind elementary operations on matrices
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High School What Does 'Simultaneous' Mean in Linear Equations?
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High School Is AB Invertible If n < m and B has a Non-Trivial Kernel?
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High School Understanding Invertible Matrices and Homogenous Systems
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Undergrad Vector Parity: +1 or -1? Scalar Difference Explained
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High School What do "linear" and "abstract" stand for?
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Undergrad Field Extensions and "Free Parameters"
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Undergrad Example of an Inseparable Polynomial .... Lovett, Page 371 ...
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High School Proof of elementary row matrix operation.
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Undergrad Existence and Uniqeness of Finite Fields ....
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MHB Existence and Uniqeness of Finite Fields .... Example from D&F ....
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Undergrad Separable Polynomials - Dummit and Foote - Proposition 37
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Undergrad Separable Polynomials - Remarks by Dummit and Foote .... ....
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Undergrad Separable Polynomials - Paul E Bland's definition and exampl
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Undergrad Splitting Fields and Separable Polynomials ....
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Undergrad Are There Nontrivial Solutions to the Matrix Equation X C X^T = C?
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MHB Solve Bracelet Problem w/14 Beads (Red, White, Blue)
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How can I resolve band assignment issues in 3D simulations using Ansoft Maxwell?
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Graduate How can I find the collision time of 2 ellipsoids that rotate
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MHB Field Extensions - Dummit and Foote - Exercise 13, Section 13.2 .... ....
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Undergrad Building a Unitary Matrix from a Non-Unitary Matrix
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MHB Help with Dummit & Foote Exercise 1, Section 13.2 - Algebraic Extensions
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MHB Algebraic Extensions - Dummit and Foote, Propositions 11 and 12 .... ....
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Undergrad Algebraic Extensions - Dummit and Foote, Propn 11 and 12 ....
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Undergrad Why is the dot product equivalent to matrix multiplication?
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MHB Splitting Fields - Example 3 - D&F Section 13.4, pages 537 - 538
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Undergrad Tensor Invariance and Coordinate Variance
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Undergrad Splitting Fields - Example 3 - D&F Section 13.4, pages 537 -
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MHB Basic Theory of Field Extensions - Exercise from D&F ....
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Undergrad Affine transformation and coordinates of maps
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Undergrad Similar Polygon Comparison for School Project
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Undergrad Algebraic Extensions - Lovett, Example 7.2.7 .... ....
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Graduate 4th order tensor inverse and double dot product computation
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MHB How Do You Solve the Equation 183997272.140609=SUM((X/PI())/SQRT(9)/16)?
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MHB Field Extensions - Remarks by Lovett - Page 326 .... ....
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Undergrad Field Extensions - Remarks by Lovett - Page 326 .... ....
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Undergrad Field Extensions - Lovett, Theorem 7.1.10 - Another question
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MHB Fields and Field Extensions - Dummit and Foote, Ch. 13 .... ....
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Undergrad Understanding Extension Fields & Polynomials
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Undergrad Why Avoid Low Values of h in Derivative Estimations?
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Graduate Relation between Vector Norms in Cylindrical and Cartesian Coordinates
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Undergrad Difference between an Algebra and a Vector space
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Undergrad Fields and Field Extensions - Dummit and Foote, Ch. 13 .... .
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Undergrad Group Theory: Multiplicative Cosets Explained
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MHB Field Extensions - Lovett, Theorem 7.1.10 .... ....
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Undergrad Fields and Field Extensions - Lovett, Chapter 7 .... ....
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Undergrad Why must an isomorphism between 2Z and 3Z result in mu(2) = +/- 3?
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MHB Fields and Field Extensions - Lovett, Chapter 7 .... ....
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Graduate Galois theorem in general algebraic extensions
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Undergrad How Do I Prove Polynomials Span P2?
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Undergrad Does this theorem need that Ker{F}=0?
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Undergrad Field Extensions - Lovett, Theorem 7.1.10 .... ....
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High School Singular Matrices: Transpose & Its Impact
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Undergrad Kronecker's Theorem - Anderson and Feil, Theorem 42.1
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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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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 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 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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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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