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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Conditions so that the determinant is zero
- mathmari
- · Replies 14 ·
Mappings - Similarity transformations
- mathmari
- · Replies 9 ·
Checking properties of reflections, rotations, and similitude mappings
- mathmari
- · Replies 22 ·
Undergrad Nice intro to connections between algebra and geometry
- SVN
- · Replies 4 ·
Rotation around an arbitrary point
- mathmari
- · Replies 8 ·
Finding the Centroid of a Triangle Using Coordinates
- mathmari
- · Replies 12 ·
Find XYZ for Tip of Vector Given Info on 2 Other Vectors w/ Tails at Same Point
- LMHmedchem
- · Replies 3 ·
How Do You Find the Equation of a Polar Line for a Circle with Given Points?
- mathmari
- · Replies 8 ·
How to Calculate the Distance Between Parallel Lines in Hesse Normal Form?
- mathmari
- · Replies 8 ·
How to Calculate the Equation of a Tangent Line to a Circle?
- mathmari
- · Replies 3 ·
Graduate Getting as close as possible to a solution (system of equations)?
- tjosan
- · Replies 4 ·
High School Field extension degree of Q(ζ) over Q in Example 47.7
- Math Amateur
- · Replies 4 ·
Field extension degree [Q(ζ):Q] = 2 in Anderson and Feil 47.7
- Math Amateur
- · Replies 2 ·
Why is Aut(ℝ) the trivial group?
- Math Amateur
- · Replies 5 ·
Why does irreducibility of f imply deg(f) = |F(α) : F| in Theorem 47.1?
- Math Amateur
- · Replies 2 ·
Undergrad Why does irreducibility of f imply deg(f) = |F(α):F|?
- Math Amateur
- · Replies 6 ·
Automorphisms of the complex numbers Aut(ℂ)
- Math Amateur
- · Replies 8 ·
Undergrad Why is √6 chosen for the basis of ℚ(√2, √3)?
- Math Amateur
- · Replies 2 ·
Differences in notation for F[α] and F(α) between textbooks
- Math Amateur
- · Replies 2 ·
Basis for Q(√2, √3): why √6 in Anderson and Feil 44.2
- Math Amateur
- · Replies 1 ·
Undergrad Why is there a Matrix A that satisfies F(x,y)=<Ax,y>?
- nightingale123
- · Replies 4 ·
Change from cartesian coordinates to cylindrical and spherical
- akkex
- · Replies 2 ·
Undergrad Finding the inverse of a matrix using transformations?
- parshyaa
- · Replies 8 ·
Undergrad Divergent Sums of Linearly Independent Elements
- Gear300
- · Replies 14 ·
Graduate Dot Product of Streaming vectors
- zheng004
- · Replies 18 ·
Undergrad Normal extensions and Theorem 45.6 in Anderson and Feil
- Math Amateur
- · Replies 7 ·
Anderson and Feil Theorem 45.6: why K equals F(α) for normal extensions
- Math Amateur
- · Replies 1 ·
Undergrad What does the multiplication of matrix represents?
- parshyaa
- · Replies 2 ·
How Do Planes Intersect in Various Linear Systems?
- srg263
- · Replies 6 ·
Undergrad Why must algebraic elements be roots of irreducible polynomials?
- Math Amateur
- · Replies 9 ·
Fixed field of Aut(K/F) in Galois theory
- Math Amateur
- · Replies 2 ·
Splitting Fields: Anderson and Feil, Theorem 45.4
- Math Amateur
- · Replies 6 ·
What is the method for solving vector problems with component form and addition?
- Coder74
- · Replies 5 ·
Undergrad Anderson and Feil Theorem 45.4 on splitting fields
- Math Amateur
- · Replies 3 ·
What is the Linear Equation for the Yield of an Orange Grove?
- mathdad
- · Replies 6 ·
Undergrad Why is the identity matrix needed in (sI−A)X(s) = BU(s)?
- MikeSv
- · Replies 7 ·
Undergrad Galois Theory - Fixed Field of F and Definition of Aut(K/F)
- Math Amateur
- · Replies 2 ·
Undergrad Galois theory Proposition 11.1.11: is U(F) a typo for U(K)?
- Math Amateur
- · Replies 5 ·
Fixed subfield of K by automorphism group H in Lovett 11.1.11
- Math Amateur
- · Replies 2 ·
Galois Theory: Textbook recommendations?
- Kiwi1
- · Replies 2 ·
Undergrad Aut(K/Q(∛13)) ≅ Z₂ and mapping roots in Lovett example 11.1.10
- Math Amateur
- · Replies 6 ·
High School Associativity of Matrix multiplication
- Buffu
- · Replies 15 ·
Minimal polynomial of √2 + √3 and field automorphisms
- Math Amateur
- · Replies 2 ·
Undergrad Roots of minimal polynomial x^4 - 10x^2 + 1 for √2 + √3
- Math Amateur
- · Replies 5 ·
Undergrad Developing Intuition Behind Affine Subspaces: A Sample Problem
- Erik109
- · Replies 6 ·
High School Why does every subfield of Complex number have a copy of Q?
- Buffu
- · Replies 33 ·
High School Vector Space over Field of Real Numbers
- Buffu
- · Replies 7 ·
High School ##AB = I \implies BA = I##, for square matricies ##A,B##
- Buffu
- · Replies 15 ·
Nested Matrix Elements: Define \Gamma^{\dagger}?
- topsquark
- · Replies 1 ·
Undergrad Intuition behind elementary operations on matrices
- Mr Real
- · Replies 48 ·
High School What Does 'Simultaneous' Mean in Linear Equations?
- mech-eng
- · Replies 1 ·
High School Is AB Invertible If n < m and B has a Non-Trivial Kernel?
- Buffu
- · Replies 6 ·
High School Understanding Invertible Matrices and Homogenous Systems
- Buffu
- · Replies 15 ·
Undergrad Why do vectors have parity +1 and pseudovectors parity -1?
- Diksha17
- · Replies 1 ·
High School What do "linear" and "abstract" stand for?
- Buffu
- · Replies 12 ·
Undergrad Field Extensions and "Free Parameters"
- Math Amateur
- · Replies 18 ·
Undergrad Lovett Example 7.7.4: inseparable polynomial m(t) = t³ - x
- Math Amateur
- · Replies 3 ·
High School Proof of elementary row matrix operation.
- Buffu
- · Replies 9 ·
Undergrad Finite field dimension and multiplicative group order
- Math Amateur
- · Replies 3 ·
Finite field cardinality and multiplicative group order in Dummit and Foote
- Math Amateur
- · Replies 2 ·
Undergrad Separable Polynomials - Dummit and Foote - Proposition 37
- Math Amateur
- · Replies 5 ·
Undergrad Separable polynomials and derivatives in characteristic p
- Math Amateur
- · Replies 1 ·
Undergrad Separable Polynomials - Paul E Bland's definition and exampl
- Math Amateur
- · Replies 8 ·
Undergrad Comparing definitions of separable polynomials in Dummit-Foote and Bland
- Math Amateur
- · Replies 6 ·
Undergrad Are There Nontrivial Solutions to the Matrix Equation X C X^T = C?
- vibe3
- · Replies 9 ·
Solve Bracelet Problem w/14 Beads (Red, White, Blue)
- mrtwhs
- · Replies 1 ·
Graduate How can I resolve band assignment issues in 3D simulations using Ansoft Maxwell?
- Farh
- · Replies 3 ·
Graduate What if the (semi) field characteristic of N is not zero?
- Cathr
- · Replies 3 ·
Graduate How can I find the collision time of 2 ellipsoids that rotate
- Guy Ab
- · Replies 1 ·
Why is x^2 + 1 an Irreducible Polynomial?
- mathdad
- · Replies 7 ·
Dummit and Foote 13.2 exercise 13: showing √³2 is not in F
- Math Amateur
- · Replies 5 ·
Undergrad Building a Unitary Matrix from a Non-Unitary Matrix
- MrRobotoToo
- · Replies 2 ·
Dummit and Foote exercise 1.13.2 on algebraic extensions
- Math Amateur
- · Replies 2 ·
Consistency of propositions 11 and 12 on algebraic extensions in Dummit and Foote
- Math Amateur
- · Replies 2 ·
Undergrad Propositions 11 and 12 on algebraic extensions in Dummit and Foote
- Math Amateur
- · Replies 3 ·
Undergrad Why is the dot product equivalent to matrix multiplication?
- rdgn
- · Replies 4 ·
Why extension degree is 2 in D&F splitting field example
- Math Amateur
- · Replies 2 ·
Undergrad Tensor Invariance and Coordinate Variance
- vanhees71
- · Replies 6 ·
Undergrad Why is the degree of extension exactly 2 in Dummit-Foote example 3?
- Math Amateur
- · Replies 2 ·
Why is irreducibility of p(x) needed in Dummit-Foote exercise 13.1.1?
- Math Amateur
- · Replies 2 ·
Undergrad Affine transformation and coordinates of maps
- H Psi equal E Psi
- · Replies 1 ·
Undergrad Similar Polygon Comparison for School Project
- YouWayne
- · Replies 9 ·
Undergrad Minimum polynomial of √2 + √3 in Lovett example 7.2.7
- Math Amateur
- · Replies 4 ·
Graduate 4th order tensor inverse and double dot product computation
- Experience111
- · Replies 1 ·
How Do You Solve the Equation 183997272.140609=SUM((X/PI())/SQRT(9)/16)?
- waptrick
- · Replies 2 ·
Undergrad Distinction between coordinates and vectors
- Mr Davis 97
- · Replies 7 ·
Why does a(x)q(x) bar equal 1 imply a(α)q(α) = 1?
- Math Amateur
- · Replies 4 ·
Undergrad Why does ā(x)q̄(x) = 1 in quotient ring imply a(α)q(α) = 1?
- Math Amateur
- · Replies 1 ·
Solve Word Problem w/ Matrices: Chapter I
- megacat8921
- · Replies 3 ·
Undergrad Lovett theorem 7.1.10: minimal degree of denominator in field extension
- Math Amateur
- · Replies 6 ·
Undergrad Why are polynomials defined the way they are in algebra?
- Mr Davis 97
- · Replies 2 ·
Why does π being a homomorphism matter for p(x̄) = p̄(x)?
- Math Amateur
- · Replies 2 ·
Undergrad Why is F[x]/⟨p(x)⟩ called an extension field of F?
- Mr Davis 97
- · Replies 1 ·
Undergrad Why Avoid Low Values of h in Derivative Estimations?
- Ethan Singer
- · Replies 2 ·
Graduate Relation between Vector Norms in Cylindrical and Cartesian Coordinates
- LagrangeEuler
- · Replies 2 ·
Undergrad Difference between an Algebra and a Vector space
- Milsomonk
- · Replies 2 ·
Undergrad Why does p(x̄) = p̄(x) depend on π being a homomorphism?
- Math Amateur
- · Replies 4 ·
Undergrad Why do rings use additive cosets instead of multiplicative cosets?
- Mr Davis 97
- · Replies 2 ·
Why is the minimal polynomial irreducible in Lovett 7.1.10?
- Math Amateur
- · Replies 2 ·
Undergrad Why is Q[x]/(x²-5) equal to Q[√5]?
- Math Amateur
- · Replies 15 ·