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 Can I use back substitution to invert a matrix?

  • NewStudent200
  • · Replies 3 ·
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3

Graduate Residue Problem: Seeking Alternative Solutions

  • Fisicks
  • · Replies 2 ·
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2

Graduate How Can College Students Master the Math Behind Kalman Filters?

  • uglyoldbob
  • · Replies 3 ·
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3

Graduate Number of Solutions to d(p) vs F(n) Modulo Prime?

  • flouran
  • · Replies 14 ·
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14

Undergrad Why mod 11 fails for finding the last digit of 2222^50 + 7777^16

  • johnnyICON
  • · Replies 11 ·
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11

Undergrad Linear Combinations: Finding Vectors of (x,y)

  • hahatyshka
  • · Replies 1 ·
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1

Graduate A couple of Infinite Series questions

  • Ubinunc
  • · Replies 16 ·
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16

Undergrad Using Cramer's rule with triangular systems and zero determinants

  • GimB0id
  • · Replies 4 ·
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4

High School What is a Parallel Unit Vector and How is it Calculated?

  • I_am_no1
  • · Replies 8 ·
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8

Graduate Landau Notation: Writing Functions in Terms of Other Functions

  • flouran
  • · Replies 3 ·
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3

Graduate Twin Prime Sieve - A Unique and Efficient Method for Generating Twin Primes

  • Rudy Toody
  • · Replies 5 ·
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5

Graduate How is Isomorphism Related to Cayley's Theorem?

  • alexandrabel
  • · Replies 1 ·
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1

Graduate Nice little proof, can any one do it?

  • rusticle
  • · Replies 5 ·
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5

Graduate Find a permutation of order 15 in S8.

  • Charles007
  • · Replies 5 ·
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5

Undergrad Linear transformation between bases

  • gothlev
  • · Replies 4 ·
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4

Graduate How to find just one permutation in s8

  • Charles007
  • · Replies 1 ·
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1

Undergrad Construction of lines from points

  • exmachina
  • · Replies 41 ·
2
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41

Graduate Group Action and a Cartesian Product

  • chaotixmonjuish
  • · Replies 4 ·
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4

High School Finding the adjugate of a 2×2 matrix

  • Charles007
  • · Replies 4 ·
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4

Undergrad Consisity of non-homogenous systems of linear equations

  • Este
  • · Replies 5 ·
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5

Graduate What to make out of series like 1+2+3+ = -1/12 ?

  • guhan
  • · Replies 16 ·
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16

Graduate Must every linear operator have eigenvalues? If so, why?

  • ygolo
  • · Replies 16 ·
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16

Graduate Geometric intuition for eigenvalues and eigenvectors of symmetric matrices

  • bPawn
  • · Replies 1 ·
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1

Graduate Equation with Bessel functions written by 8-year-old

  • confusedmon
  • · Replies 8 ·
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8

High School Prove Square of Integer Ends in 0, 1, 4, 5, 6, 9

  • Martin Bashir
  • · Replies 2 ·
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2

Undergrad How Can I Understand 3D Rotation Matrices Like 2D?

  • likephysics
  • · Replies 1 ·
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1

Graduate Proof of inner product for function space

  • SFB
  • · Replies 3 ·
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3

Undergrad How Can I Differentiate Various Group Types in Algebra?

  • Charles007
  • · Replies 6 ·
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6

Graduate Solution Guide for Hoffman and Kunze Problems: Does it Exist?

  • CoachZ
  • · Replies 3 ·
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3

Graduate Conjugate of a matrix and of a function

  • DeepSeeded
  • · Replies 5 ·
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5

Graduate Norm of a Function vs. Length of a Vector

  • pr0me7heu2
  • · Replies 3 ·
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3

Graduate Relationship between Hermitian inner product and angle between complex vectors

  • raja0088
  • · Replies 1 ·
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1

Graduate Lorentz Force Equation: Geometric Interpretation

  • Somefantastik
  • · Replies 2 ·
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2

Undergrad Does Order Matter in Cyclic Subgroups/Groups?

  • Gear300
  • · Replies 4 ·
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4

Graduate Can I put symmetric doubling functions for algebraic numbers in a matrix?

  • noogies
  • · Replies 2 ·
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2

Graduate How can we use induction to prove that (xy)^{3} = y^{3}x^{3} for all x,y in G?

  • matticus
  • · Replies 2 ·
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2

Undergrad Prove that 12 divides n^2-1 when gcd(n,6)=1

  • Fisicks
  • · Replies 4 ·
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4

Graduate Getting comfortable with homological algebra

  • Tiger99
  • · Replies 2 ·
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2

Graduate Eigenvalue with multiplicity k resulting in k orthogonal eigenvectors?

  • el_llavero
  • · Replies 4 ·
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4

Graduate Polar Decompositions: Purpose of sqrt(T*T)

  • evilpostingmong
  • · Replies 2 ·
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2

Graduate Function norm and root mean square for sin(x) on [0,π]

  • squenshl
  • · Replies 2 ·
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2

Undergrad Fundamental Theorem of Arithmetic Problem

  • Fisicks
  • · Replies 14 ·
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14

Graduate Why does isomorphism preserve the group operation?

  • jeff1evesque
  • · Replies 8 ·
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8

Undergrad Confusing about linearity and nonlinearity

  • KFC
  • · Replies 2 ·
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2

Graduate Uniqueness Theorem for homogenous linear ODEs

  • Crosson
  • · Replies 5 ·
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5

Graduate What does <a, b, c> mean for a set in group theory?

  • Gear300
  • · Replies 4 ·
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4

Graduate Non-uniform bi-linear interpolation

  • ponjavic
  • · Replies 2 ·
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2

Graduate I dont get the point of pseudovectors

  • StatusX
  • · Replies 7 ·
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7

Undergrad LU Decomposition: Calculating Determinant of Square Matrix (Example Included)

  • demipaul
  • · Replies 1 ·
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1

Graduate How to Diagonalize a 9x9 Matrix with Unitary Vectors?

  • Ojisan
  • · Replies 6 ·
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6

Undergrad Null matrix and invertible matrix

  • seema283k
  • · Replies 1 ·
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1

Undergrad Geometrical interpretation of dot product (trying to prove)

  • Дьявол
  • · Replies 17 ·
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17

Graduate Verifying Noncyclic Abelian Subgroup of S4

  • Gear300
  • · Replies 6 ·
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6

Undergrad Innner products and basis representation

  • iontail
  • · Replies 5 ·
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5

Graduate Finding r in Paillier cryptosystem: c = g^m * r^N mod N^2

  • vanvincent
  • · Replies 5 ·
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5

Graduate What Is the Correct Form of the Cauchy-Schwarz Inequality?

  • EngWiPy
  • · Replies 10 ·
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10

Graduate Eigenvalues and eigenvectors of this matrix

  • shouvikdatta8
  • · Replies 1 ·
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1

Graduate Why is Ax in col(A) if (A^T)Ax=0

  • horefaen
  • · Replies 2 ·
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2

Graduate Reduce P = A(ATA)-1AT to P = BBT

  • squenshl
  • · Replies 1 ·
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1

Graduate What is the meaning of the subscript in the polygamma function?

  • rman144
  • · Replies 1 ·
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1

Graduate What Is a Lie Group Without an Identity Matrix Called?

  • Pythagorean
  • · Replies 3 ·
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3

Graduate Describing matrix requirements for projection matrices P and B

  • squenshl
  • · Replies 2 ·
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2

Undergrad How to find two endpoints of a line?

  • rakeshthp
  • · Replies 5 ·
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5

Graduate Do hyperreal numbers satisfy the same inequalities recursively?

  • Phrak
  • · Replies 10 ·
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10

Graduate Conjecture:fundamental mathematical group

  • SW VandeCarr
  • · Replies 71 ·
3
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71

Graduate Transformation to flip handedness of a 4-vector

  • Gza
  • · Replies 2 ·
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2

Undergrad Column Space and Pivot Columns in Reduced Matrices

  • horefaen
  • · Replies 1 ·
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1

Undergrad Simple Proof Check - Number Theory

  • Fisicks
  • · Replies 4 ·
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4

Graduate Does the identity axiom 1v = v follow from other vector space axioms?

  • AxiomOfChoice
  • · Replies 9 ·
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9

Undergrad Is it possible to determine if a number is a perfect square in different bases?

  • srijithju
  • · Replies 5 ·
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5

Graduate Why Are SU(3) Generators Traceless and Limited to Two Diagonal Matrices?

  • jacobrhcp
  • · Replies 6 ·
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6

Undergrad How can I find an endorser for my prime number papers on ArXiv?

  • Lecopantica
  • · Replies 3 ·
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3

Undergrad How can a column represent a vector in linear algebra?

  • vijay_singh
  • · Replies 4 ·
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4

Graduate Proving the Finiteness of Fermat Primes

  • chhitiz
  • · Replies 27 ·
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27

Graduate Is the only difference between functions just a change of basis?

  • Monocles
  • · Replies 1 ·
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1

Undergrad Is There Always a Prime Number Between n and n! for n>2?

  • theIBnerd
  • · Replies 8 ·
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8

Graduate Can We Obtain the Form of L from Z(u)?

  • zetafunction
  • · Replies 1 ·
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1

Graduate I came across this Proposition in my book, and I know it's something

  • lttlbbygurl
  • · Replies 1 ·
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1

High School How do i get the point of intersection of a line and a circle?

  • rakeshthp
  • · Replies 3 ·
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3

High School Solving Linear Equations: Expanding Brackets, Subbing Values

  • TheAkuma
  • · Replies 8 ·
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8

Graduate Irreducible Representations of so(4,C)

  • aziz113
  • · Replies 2 ·
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2

Graduate Numerical algorithms for finding an eigenvector

  • jostpuur
  • · Replies 4 ·
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4

Graduate Is 1|V⟩ = |V⟩ provable from Shankar's vector space axioms?

  • AxiomOfChoice
  • · Replies 1 ·
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1

Undergrad Is a symmetric matrice allways nonsingular?

  • hyper
  • · Replies 1 ·
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1

Graduate Can every real number be a sum of two squares?

  • JanClaesen
  • · Replies 14 ·
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14

Undergrad Matrix determinant operator commutative?

  • el_llavero
  • · Replies 3 ·
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3

Graduate Proving Self-Adjointness in Finite-Dimensional Vector Spaces with Inner Products

  • evilpostingmong
  • · Replies 8 ·
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8

Graduate Why is Schwarz inequality trivial when u or v equals zero?

  • Rasalhague
  • · Replies 6 ·
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6

Graduate Representing 2D vectors as Clifford multivectors and projecting back

  • PeteKH
  • · Replies 4 ·
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4

Graduate Optimal division of a matrix for processing

  • sam_wilson
  • · Replies 4 ·
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4

Undergrad Group (Associativity of Binary Operators)

  • jeff1evesque
  • · Replies 1 ·
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1

Undergrad Why Is QQ^T Singular for a Matrix with Orthonormal Columns?

  • hotvette
  • · Replies 5 ·
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5

Graduate Coprime pythagorean quadruples or higher tuples?

  • JesseM
  • · Replies 4 ·
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4

Graduate Show every group of order 77 has elements of order 7 and 11

  • matticus
  • · Replies 8 ·
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8

Undergrad What is the Quotient Group A/B?

  • pellman
  • · Replies 2 ·
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2

Graduate Legendre and Riemann: A Conjecture Comparison

  • daniel tisdal
  • · Replies 6 ·
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6

Graduate Relating to Duality in Vector Spaces

  • mosenja
  • · Replies 7 ·
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7

Undergrad Number Theory integer roots Problem

  • pzona
  • · Replies 16 ·
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16

Undergrad Does the mediant of two fractions always lie between them?

  • Helios
  • · Replies 1 ·
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1

Graduate Rotation matrices for arbitrary angles around two specific axes

  • owlpride
  • · Replies 4 ·
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4