Linear and Abstract Algebra Forum

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.

Threads

Undergrad Finding a matrix for a linear transformation in a given basis

  • lukaszh
  • · Replies 3 ·
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3

Undergrad What Are the Possible Sums of Prime Number Pairs?

  • Loren Booda
  • · Replies 2 ·
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2

Graduate Tensor Product of V1 and V2 in Vector Space V: 0 Intersection Required?

  • Werg22
  • · Replies 3 ·
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3

High School Core of matrix (pure translatio)

  • maros522
  • · Replies 3 ·
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3

Undergrad What does the 'X' mean in the Mueller matrix rotation equation?

  • islahna
  • · Replies 5 ·
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5

Graduate Proof, intersection and sum of vector spaces

  • lukaszh
  • · Replies 4 ·
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4

Graduate Apparent fallacy in linear operator theory

  • neelakash
  • · Replies 1 ·
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1

Graduate Why eigenvalue specification reduces the no. of LI equations?

  • neelakash
  • · Replies 1 ·
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1

Graduate Is e^ix multivalued, roots of unity, etc

  • okkvlt
  • · Replies 6 ·
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6

Graduate Solving AX=B with Preconditioned Conjugate Gradient Algorithm

  • callingearth
  • · Replies 2 ·
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2

Graduate Isomorphism between R^inf and a proper subset of R^inf

  • jojo12345
  • · Replies 4 ·
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4

Graduate Can Any Inner Product Be Defined in Infinite Dimensional Vector Spaces?

  • neelakash
  • · Replies 2 ·
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2
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9

Graduate When do objects factorize uniquely?

  • Gerenuk
  • · Replies 2 ·
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2

Graduate Direct products in category of torsion abelian groups

  • mathsss2
  • · Replies 2 ·
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2
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6

Undergrad Finding Axes of Conic Section Equation

  • aamirnshah
  • · Replies 3 ·
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3

Undergrad Does divisibility apply to imaginary numbers?

  • glass.shards
  • · Replies 5 ·
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5

Undergrad What is the identity for coplanar, non-collinear vectors?

  • atavistic
  • · Replies 8 ·
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8

Graduate Odds that two numbers are coprime

  • soandos
  • · Replies 1 ·
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1

Undergrad What are the rank conditions for consistency of a linear algebraic system?

  • cheesefondue
  • · Replies 3 ·
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3

High School How can I improve this equation to work in all cases?

  • pjhphysics
  • · Replies 8 ·
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8

Undergrad How to compute P.Q and Q.P for permutations of (1,2,3,4,5)

  • FatTail
  • · Replies 4 ·
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4

Graduate How Can I Derive a Set of 3x3 Matrices Analogous to the Pauli Matrices?

  • Dahaka14
  • · Replies 6 ·
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6

Undergrad Is a Two by Two Matrix a Basis if ad - bc = ±1?

  • soandos
  • · Replies 11 ·
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11

Graduate Happy holidays,BenDecomposing tensor product of GL(2,C) representations

  • swallowtail
  • · Replies 1 ·
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1

Undergrad Linear Algebra transformation Question

  • samspotting
  • · Replies 14 ·
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14

Graduate Do Non-Associative Groups Exist and What Are Their Applications?

  • Winzer
  • · Replies 3 ·
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3

Undergrad Why 30 is the largest integer such that none of its ?

  • HussamLawen
  • · Replies 2 ·
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2

Undergrad Relation between rank and number of non-zero eigen values.

  • NaturePaper
  • · Replies 11 ·
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11

Undergrad Linear Transformation from R^2 to R^3

  • JG89
  • · Replies 4 ·
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4

Graduate Evaluating the sum and integral of s^-s

  • Loren Booda
  • · Replies 2 ·
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2

Graduate Questions about group presentations

  • samkolb
  • · Replies 4 ·
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4

Graduate Upper limit of cross terms in vector space expansion

  • norbert
  • · Replies 2 ·
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2

Undergrad Does group theory deal with asymmetry?

  • jjoensuu
  • · Replies 2 ·
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2

Undergrad Why does (a·b)c = (cb^T)a for vectors?

  • Apteronotus
  • · Replies 7 ·
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7

Undergrad Finding Arbitrary nth Roots of -1 Algebraically

  • soandos
  • · Replies 6 ·
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6

Graduate What is group theory all about?

  • oldman
  • · Replies 6 ·
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6

Undergrad Matrix Multiplication and Addition with Identity and Zero Matrices

  • fazal
  • · Replies 3 ·
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3

Graduate Relating Two-Dimensional Vectors and Complex Numbers

  • Sollytear
  • · Replies 6 ·
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6

Undergrad Solving Equations Involving A⁻¹, B⁻¹ and C⁻¹

  • fazal
  • · Replies 3 ·
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3

Graduate Root of Non-Linear Eqn (Numerical Method)

  • Apteronotus
  • · Replies 1 ·
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1

Graduate Zeta function in the critical strip

  • TheOogy
  • · Replies 10 ·
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10

Graduate Why define the dual basis with the Kronecker delta

  • Etenim
  • · Replies 2 ·
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2

Graduate Is the Inverse of a Matrix a Continuous Function?

  • tjm7582
  • · Replies 9 ·
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9

Undergrad Quadratic forms, diagonalization

  • student111
  • · Replies 3 ·
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3

Undergrad Calculating Pi in Binary: How Many Decimals Do I Need?

  • Priha
  • · Replies 9 ·
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9

Graduate Raising Matrices to power of n. (complex)

  • Epsillon
  • · Replies 7 ·
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7

Undergrad Mappings and Inverses: More Than One Left Inverse?

  • kidsmoker
  • · Replies 2 ·
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2

Graduate What is the definition of R in the tensor product construction?

  • amicciulla
  • · Replies 1 ·
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1

Undergrad Yes, that was exactly what I couldn't get. Thank you for clarifying it for me!

  • Daveyboy
  • · Replies 10 ·
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10

Undergrad Why do books distinguish ordered bases from unordered ones?

  • dmuthuk
  • · Replies 3 ·
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3

Undergrad Three Digit Prime Number Puzzle: Forming Primes with All Prime Digits

  • Loren Booda
  • · Replies 14 ·
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14

Graduate What is the proof for GCD(n.m)=1 if 2^m-1 and 2^n-1 have a common divisor of 1?

  • HussamLawen
  • · Replies 3 ·
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3

Undergrad Can a Matrix Be Expressed as a Sum of Diagonalizable and Nilpotent Matrices?

  • MathIdiot
  • · Replies 7 ·
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7

Graduate How Accurate Are Partial Sums in Estimating e^N?

  • Nurdan
  • · Replies 1 ·
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1

Graduate Hermitian vs. self-adjoint operators

  • Heirot
  • · Replies 10 ·
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10

Undergrad Are Column Vectors in AB Unchanged if Linearly Independent?

  • only_huce
  • · Replies 1 ·
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1

Graduate Pattern in mirror-inverted 3D numbers

  • Rhuben
  • · Replies 2 ·
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2

Graduate Su(2) Lie Algebra in SO(3): Why Choose Omega/2?

  • sunkesheng
  • · Replies 6 ·
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6

Graduate Uniquely n-Divisible and Torsionfree Groups in Exact Sequences

  • mathsss2
  • · Replies 13 ·
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13

Graduate Deriving tensor components of the Hodge dual of a p-vector

  • guhan
  • · Replies 2 ·
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2

Graduate Can you solve x = y^y for y?

  • soandos
  • · Replies 50 ·
2
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50

Graduate Carmichael Number: Proving $(d+p)(p-1)$ Divisor of $q-1$

  • peteryellow
  • · Replies 2 ·
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2

Undergrad Finding a pattern for prime numbers

  • ƒ(x)
  • · Replies 28 ·
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28

Graduate Identity of Zeta function

  • mhill
  • · Replies 1 ·
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1

Undergrad Can You Solve the Equation X^2 + Y^2 + Z^2 = NXYZ for Natural N?

  • hadi amiri 4
  • · Replies 2 ·
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2

Graduate Imaginary Zeros of Zeta Function

  • rman144
  • · Replies 4 ·
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4

Graduate Mobius Inversion, finite subgroup

  • mathsss2
  • · Replies 1 ·
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1

Undergrad Chance of random walk returning to origin

  • Loren Booda
  • · Replies 14 ·
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14

Graduate Where Fibonacci numbers surpass prime numbers

  • Loren Booda
  • · Replies 4 ·
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4

Graduate Symmetric group (direct product and decomposition)

  • Symmetryholic
  • · Replies 13 ·
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13

Undergrad Linear Algerba - Finding linearly independent vectors

  • Moomax
  • · Replies 5 ·
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5

Undergrad Why Use the Last Row of the Elimination Matrix for Left Nullspace?

  • only_huce
  • · Replies 1 ·
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1

Graduate Solving a Puzzling Problem: No A Exists for Symmetric Matrix B

  • BOS200011
  • · Replies 7 ·
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7

Graduate If the z-transform of x[n] is X(z)

  • symsane
  • · Replies 4 ·
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4

Undergrad Systems of algebraic equations

  • jimmy1
  • · Replies 9 ·
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9

Graduate Constructing everywhere defined unbounded operators on Hilbert spaces

  • cogito²
  • · Replies 14 ·
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14

Graduate Difficult polynomial and determinant formula

  • jostpuur
  • · Replies 26 ·
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26

Graduate What is the Concept of Zero Double Trace in Tensor Analysis?

  • kauw7
  • · Replies 4 ·
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4

Undergrad Numerically stable method for inverting a 6x6 matrix

  • Zurtex
  • · Replies 14 ·
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14

Undergrad Is (x^4)+1 Reducible over Z5 and Z?

  • billybob12345
  • · Replies 3 ·
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3

Graduate Why is the Gram-Schmidt Process Numerically Unstable?

  • ModernLogic
  • · Replies 2 ·
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2

Graduate Galois extension, lattice of subfields

  • mathsss2
  • · Replies 1 ·
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1

Undergrad How is a matrix diagonalised?

  • eluu
  • · Replies 13 ·
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13

Graduate Isomorphism of su(2) and sl(2,C): Tensor w/ Complex Numbers

  • koolmodee
  • · Replies 6 ·
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6

Undergrad Is ||x||₂ · ||A||₂ = ||Ax||₂?

  • ahamdiheme
  • · Replies 1 ·
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1

Undergrad Finding a vector orthogonal to others

  • logarithmic
  • · Replies 18 ·
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18

Graduate Irreducible polynomial, cyclic group

  • mathsss2
  • · Replies 2 ·
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2

Graduate What Are the Subfields of F=F_{p^{18}} and Their Lattice Representation?

  • mathsss2
  • · Replies 2 ·
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2

Graduate Proving Vector Space Relationships in WU{A} and WU{B}

  • LAINHELL
  • · Replies 1 ·
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1

Graduate What are the properties of valuation rings and their ideals?

  • mathsss2
  • · Replies 1 ·
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1

Graduate Solve a system of linear equations Ax=kb

  • turbulent1
  • · Replies 3 ·
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3

Graduate How Can You Define an Inner Product to Orthogonalize Arbitrary Basis Matrices?

  • turin
  • · Replies 18 ·
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18

Graduate Z[i]-module Question: Finding Torsion and Integer r for Module M

  • mathsss2
  • · Replies 1 ·
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1

Graduate What is the Significance of the Orbit of P in Sylow's Theorems?

  • mathsss2
  • · Replies 1 ·
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1

Undergrad When does Ax=b have solutions?

  • CalculusSandwich
  • · Replies 8 ·
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8

Undergrad Finding Basis for Matrix Transformation: SBT = E_k

  • Marin
  • · Replies 2 ·
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2

Graduate Number of primative roots in finite fields of order p^n

  • Bourbaki1123
  • · Replies 1 ·
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1

Graduate Vector product and Lie brackets on C³

  • koolmodee
  • · Replies 2 ·
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2