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.
Undergrad What Is the Study of Homomorphisms from Abstract Groups to GL(n)?
  • zwoodrow
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Undergrad The limit of the perimeter of a Koch snowflake as s(0) goes to zero
  • nomadreid
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Finding z-(1/z) Given z=r(cosx+isinx)
  • araz1
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Is z + z¯ and z × z¯ Real for Any Complex Number z?
  • Yordana
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How Do You Solve These Simultaneous Equations?
  • Yordana
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Undergrad What are the significant angles between intersecting planes in 4D space?
  • Hornbein
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Undergrad Proof that if T is Hermitian, eigenvectors form an orthonormal basis
  • Hall
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What is the GCD and LCM of 35280 and 4158?
  • karush
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Invariance of Asymmetry under Orthogonal Transformation
  • PkayGee
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Graduate Vectors as geometric objects and vectors as any mathematical objects
  • Hall
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Is Every Group of Order 25 Cyclic?
  • karush
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Could you prove that f(A)>=0 whenever A>0?
  • DrLiangMath
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Undergrad Linear independence of three vectors
  • Salmone
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*elements and generators of U(14)
  • karush
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Graduate Solving algebraic equations that cannot be solved in radicals
  • Demystifier
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Undergrad Proof about a positive definite matrix
  • Jamister
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Graduate Anti-dual numbers and what are their properties?
  • Anixx
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Graduate Tensor product matrices order relation
  • Jufa
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Undergrad Understanding zero divisors & ##\mathbb{Z_m}## in Ring Theory
  • chwala
  • · Replies 55 ·
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How Do You Map Matrices to Complex Numbers in Linear Algebra?
  • Eric Machisi
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Graduate Eigenvalue of the sum of two non-orthogonal (in general) ket-bras
  • Jufa
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Undergrad Matrix representation for closed-form expression for Fibonacci numbers
  • murshid_islam
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Undergrad Different norms and how L1 leads to the sparsest solution
  • fog37
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Undergrad Prove the given properties - Ring Theory
  • chwala
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Undergrad Continued fractions and nested radicals
  • ajawagner
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Undergrad What is the difference between a complete basis and an overcomplete dictionary?
  • fog37
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Undergrad Is tensor product the same as dyadic product of two vectors?
  • xopek
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Undergrad What are the Eigenvalues of the Hermitian Inverse \(H^{-1}\)?
  • ergospherical
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Proving Properties of 2x2 Matrices
  • TheScienceAlliance
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Does Commutativity Hold for Matrices A and B with a Specific Matrix C?
  • TheScienceAlliance
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Maxima and Minima (vector calculus)
  • WMDhamnekar
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Undergrad Does Axler's Spectral Theorem Imply Normal Matrices?
  • boo
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Undergrad A few questions about doing a Gaussian Fit
  • btb4198
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Undergrad Determinant of a specific, symmetric Toeplitz matrix
  • Rlwe
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An Overview of the History of Tea
  • enogjini
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Undergrad How is uniqueness about the determinant proved by this theorem?
  • Hall
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High School Does this kind of square matrix exist?
  • Trollfaz
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Undergrad Confused about dot product of a and b = |a||b| if theta = 0
  • annamal
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Undergrad Graph Representation Learning: Question about eigenvector of Laplacian
  • Master1022
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Undergrad What Does the F Matrix Look Like for a Linear Bezier Curve?
  • bobtedbob
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Graduate First eigenvalue not matching, but all others are
  • member 428835
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Undergrad This is an invalid argument about eigenvalues, but why?
  • nomadreid
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Undergrad Can integers be defined as N[[sqrt(1)]]?
  • arivero
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6.2.8 {{k,4},{3,k}}=k what is k
  • karush
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High School Inductive proof for multiplicative property of sdet
  • Korybut
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Undergrad Manipulation of 2nd, 3rd & 4th order tensor using Index notation
  • chowdhury
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Undergrad The way matrices are written without boxes
  • Hall
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High School Inverse of a Vector: Find the Correct Form
  • chowdhury
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High School Is Super Commutativity Essential in Defining a Super Lie Module?
  • Korybut
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Undergrad Proof that two linear forms kernels are equal
  • Portuga
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High School Recurrence relation in a recurrence relation?
  • MevsEinstein
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Undergrad Contracted Christoffel symbols in terms determinant(?) of metric
  • George Keeling
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Undergrad Convert cylindrical coordinates to Cartesian
  • nuclearsneke
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High School One-to-many relations in group theory
  • redtree
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Undergrad What is the importance of p-Sylow subgroups in understanding group structure?
  • Santiago24
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Undergrad Generators of Galois group of ## X^n - \theta ##
  • kmitza
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High School Determinant of a transposed matrix
  • Eclair_de_XII
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Graduate How Does the Non-Equality of Kernels Imply Their Sum Equals the Vector Space?
  • Portuga
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Graduate Reason out the cross product (for the moment): a skew symmetric form
  • Trying2Learn
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Undergrad Factoring Matrices with Elementary Row Operations
  • cbarker1
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Graduate Calculating the Modal Matrix for A
  • boo
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Undergrad What Conditions Ensure the Minimal Polynomial of α Divides P in Galois Theory?
  • giulio_hep
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Graduate How to visualise complex vector spaces of dimension 2 and above
  • pellis
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Undergrad Basis of 2x2 matrices with real entries
  • LagrangeEuler
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Undergrad Proving properties of polynomial in K[x]
  • kmitza
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What Are the Possible Jordan Forms and Characteristic Polynomial of T?
  • darksidemath
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Undergrad How to find the generator of this Lie group?
  • Haorong Wu
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Group Elements of Z24: Find the Order
  • Yara Leonard
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Number of solutions for system of equations
  • bargaj
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-la.1.1.19 the augmented process
  • karush
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Undergrad Orthogonality of Eigenvectors of Linear Operator and its Adjoint
  • ughpleasenope
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Undergrad Does associativity imply bijectivity in group operations?
  • valenumr
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Graduate Need some clarifications on tensor calculus please
  • pitaly
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3.13 Compute the orders of the following groups:
  • karush
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307.8.1 Suppose Y_1 and Y_2 form a basis for a 2-dimensional vector space V
  • karush
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307.8.3 Compute A^n for the Jordan block
  • karush
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311.3.1.1 - Determinants And Cofactor Expansion
  • karush
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What are the generators of $\Bbb{Z}_6, \Bbb{Z}_8,$ and $\Bbb{Z}_{20}$?
  • karush
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Set of vectors form a vector space
  • karush
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Describes elements of D_5 using SAGE
  • karush
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Z6: Identity, Order, Inverse, Generator, Abelian/Non-Abelian, Subgroups
  • karush
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Undergrad What Is a Dyadic? - Understanding What They Are & How To Use Them
  • Trying2Learn
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Undergrad Linear Algebra 1 problem, Vector Geometry: Lines
  • Student323
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Undergrad Is This a Valid Basis for the Set of Polynomials with \( p(0) = p(1) \)?
  • Hall
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Undergrad S is set of all vectors of form (x,y,z) such that x=y or x =z. Basis?
  • Hall
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High School Proof involving two linear equations
  • RM86Z
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Undergrad How can I find all possible Jordan forms?
  • laurabon
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How Do You Solve Linear Equations with Given Coordinates?
  • Sarahq
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Graduate What is the Definition and Properties of a Cross Product in Vector Algebra?
  • Greg Bernhardt
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Undergrad Looking for a creative or quick method for finding roots in GF(p^n)
  • kmitza
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Undergrad Similarity transformation, basis change and orthogonality
  • Azad Koshur
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Undergrad Irreducible polynomials and prime elements
  • darksidemath
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Graduate Matrix Multiplication: Solving A*A'=B for Unique A(B)
  • feynman1
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Solve System Using Matrix Inverse
  • brinlin
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Undergrad Anyone knows why musical isomorphism is called so?
  • lriuui0x0
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Undergrad Finding a polynomial that has solution (root) as the sum of roots
  • swampwiz
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Undergrad Proving the Existence of Roots in Complex Polynomials
  • Delta2
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Proof of Complex Numbers: Delta*w(z, z) Explained
  • Bat1
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Finding a Basis for a Linear Subspace Orthogonal to a Given Point P in R^3
  • JWS1
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Undergrad Interesting Article Ref: Sudoku and Linear Algebraic aspects
  • WWGD
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