Linear and Abstract Algebra Forum

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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 to Calculate the Distance Between Parallel Lines in Hesse Normal Form?
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MHB How to Calculate the Equation of a Tangent Line to a Circle?
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Graduate Getting as close as possible to a solution (system of equations)?
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High School Galois Groups .... A&F Example 47.7 .... ....
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MHB Galois Groups .... A&F Example 47.7 .... ....
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MHB Groups of Automorphisms - remarks by Anderson and Feil ....
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MHB Galois Groups .... A&W Theorem 47.1 .... ....
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Undergrad Galois Groups .... A&W Theorem 47.1 .... ....
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MHB Groups of Automporphisms - Aut(C) .... Anderson and Feil Ch. 24 ....
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Undergrad Finite Extensions - A&F Example 44.2 .... ....
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MHB Basic Notation for Field Extensions .... ....
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MHB Finite Extensions - A&F Example 44.2 .... ....
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Undergrad Why is there a Matrix A that satisfies F(x,y)=<Ax,y>?
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MHB Change from cartesian coordinates to cylindrical and spherical
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Undergrad Finding the inverse of a matrix using transformations?
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Undergrad Divergent Sums of Linearly Independent Elements
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Graduate Dot Product of Streaming vectors
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Undergrad Splitting Fields: Anderson and Feil, Theorem 45.6 ....
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MHB Splitting Fields: Anderson and Feil, Theorem 45.6 ....
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Undergrad What does the multiplication of matrix represents?
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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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MHB What is the method for solving vector problems with component form and addition?
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Undergrad Splitting Fields: Anderson and Feil, Theorem 45.4 ....
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MHB What is the Linear Equation for the Yield of an Orange Grove?
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Undergrad Why is the Identity Matrix essential in Multivariable Control Theory?
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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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Graduate How can I resolve band assignment issues in 3D simulations using Ansoft Maxwell?
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Graduate What if the (semi) field characteristic of N is not zero?
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Graduate How can I find the collision time of 2 ellipsoids that rotate
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MHB Why is x^2 + 1 an Irreducible Polynomial?
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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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Undergrad Distinction between coordinates and vectors
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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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MHB Solve Word Problem w/ Matrices: Chapter I
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Undergrad Field Extensions - Lovett, Theorem 7.1.10 - Another question
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Undergrad Why are polynomials defined the way they are in algebra?
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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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