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

Is Gauss' Lemma the Key to Non-UFDs in Polynomial Rings?

  • Math Amateur
  • · Replies 1 ·
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1

Mason's question via Facebook about solving a system of equations

  • Prove It
  • · Replies 1 ·
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1

Undergrad What Is the Study of Homomorphisms from Abstract Groups to GL(n)?

  • zwoodrow
  • · Replies 3 ·
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3

Undergrad The limit of the perimeter of a Koch snowflake as s(0) goes to zero

  • nomadreid
  • · Replies 10 ·
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10

Finding z-(1/z) Given z=r(cosx+isinx)

  • araz1
  • · Replies 6 ·
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6

Is z + z¯ and z × z¯ Real for Any Complex Number z?

  • Yordana
  • · Replies 1 ·
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1

How Do You Solve These Simultaneous Equations?

  • Yordana
  • · Replies 2 ·
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2

Undergrad What are the significant angles between intersecting planes in 4D space?

  • Hornbein
  • · Replies 26 ·
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26

Undergrad Proof that if T is Hermitian, eigenvectors form an orthonormal basis

  • Hall
  • · Replies 3 ·
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3

What is the GCD and LCM of 35280 and 4158?

  • karush
  • · Replies 4 ·
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4

Invariance of Asymmetry under Orthogonal Transformation

  • PkayGee
  • · Replies 1 ·
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1

Graduate Vectors as geometric objects and vectors as any mathematical objects

  • Hall
  • · Replies 27 ·
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27

Is Every Group of Order 25 Cyclic?

  • karush
  • · Replies 1 ·
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1

Could you prove that f(A)>=0 whenever A>0?

  • DrLiangMath
  • · Replies 6 ·
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6

Undergrad Linear independence of three vectors

  • Salmone
  • · Replies 45 ·
2
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45

*elements and generators of U(14)

  • karush
  • · Replies 2 ·
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2

Graduate Solving algebraic equations that cannot be solved in radicals

  • Demystifier
  • · Replies 6 ·
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6

Undergrad Proof about a positive definite matrix

  • Jamister
  • · Replies 12 ·
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12

Graduate Anti-dual numbers and what are their properties?

  • Anixx
  • · Replies 1 ·
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1

Graduate Tensor product matrices order relation

  • Jufa
  • · Replies 1 ·
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1

Undergrad Zero divisors in product rings

  • chwala
  • · Replies 55 ·
2
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55

How Do You Map Matrices to Complex Numbers in Linear Algebra?

  • Eric Machisi
  • · Replies 2 ·
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2

Graduate Eigenvalue of the sum of two non-orthogonal (in general) ket-bras

  • Jufa
  • · Replies 13 ·
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13

Undergrad Matrix representation for closed-form expression for Fibonacci numbers

  • murshid_islam
  • · Replies 2 ·
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2

Undergrad Different norms and how L1 leads to the sparsest solution

  • fog37
  • · Replies 1 ·
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1

Undergrad Prove the given properties - Ring Theory

  • chwala
  • · Replies 14 ·
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14

Undergrad Isomorphism between continued fractions and nested radicals

  • ajawagner
  • · Replies 1 ·
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1

Undergrad What is the difference between a complete basis and an overcomplete dictionary?

  • fog37
  • · Replies 5 ·
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5

Undergrad Is tensor product the same as dyadic product of two vectors?

  • xopek
  • · Replies 4 ·
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4

Undergrad What are the Eigenvalues of the Hermitian Inverse \(H^{-1}\)?

  • ergospherical
  • · Replies 2 ·
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2

Proving Properties of 2x2 Matrices

  • TheScienceAlliance
  • · Replies 5 ·
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5

Does Commutativity Hold for Matrices A and B with a Specific Matrix C?

  • TheScienceAlliance
  • · Replies 3 ·
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3

Maxima and Minima (vector calculus)

  • WMDhamnekar
  • · Replies 1 ·
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1

Undergrad Does Axler's Spectral Theorem Imply Normal Matrices?

  • boo
  • · Replies 3 ·
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3

Undergrad A few questions about doing a Gaussian Fit

  • btb4198
  • · Replies 4 ·
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4

Undergrad Determinant of a specific, symmetric Toeplitz matrix

  • Rlwe
  • · Replies 1 ·
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1

Why does (A-cI)x equal (λ-c)x when λ is an eigenvalue?

  • enogjini
  • · Replies 2 ·
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2

Undergrad How is uniqueness about the determinant proved by this theorem?

  • Hall
  • · Replies 10 ·
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10

High School Does this kind of square matrix exist?

  • Trollfaz
  • · Replies 4 ·
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4

Undergrad Why doesn't my dot product equal |a||b| when theta = 0?

  • annamal
  • · Replies 16 ·
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16

Undergrad What does an eigenvector of the graph Laplacian represent intuitively?

  • Master1022
  • · Replies 1 ·
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1

Undergrad What Does the F Matrix Look Like for a Linear Bezier Curve?

  • bobtedbob
  • · Replies 1 ·
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1

Graduate First eigenvalue not matching, but all others are

  • member 428835
  • · Replies 8 ·
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8

Undergrad This is an invalid argument about eigenvalues, but why?

  • nomadreid
  • · Replies 8 ·
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8

Undergrad Can integers be defined as N[[sqrt(1)]]?

  • arivero
  • · Replies 25 ·
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25

6.2.8 {{k,4},{3,k}}=k what is k

  • karush
  • · Replies 3 ·
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3

High School Inductive proof for multiplicative property of sdet

  • Korybut
  • · Replies 1 ·
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1

Undergrad Writing 2nd, 3rd and 4th order tensors in index notation

  • chowdhury
  • · Replies 5 ·
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5

Undergrad The way matrices are written without boxes

  • Hall
  • · Replies 9 ·
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9

High School Inverting a tensor-vector equation with two operations

  • chowdhury
  • · Replies 24 ·
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24

High School Super Lie module definition and supercommutativity requirement

  • Korybut
  • · Replies 4 ·
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4

Undergrad Proof that two linear forms kernels are equal

  • Portuga
  • · Replies 4 ·
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4

High School Recurrence relation in a recurrence relation?

  • MevsEinstein
  • · Replies 8 ·
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8

Undergrad Contracted Christoffel symbols in terms determinant(?) of metric

  • George Keeling
  • · Replies 1 ·
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1

Undergrad Convert cylindrical coordinates to Cartesian

  • nuclearsneke
  • · Replies 6 ·
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6

High School One-to-many relations in group theory

  • redtree
  • · Replies 4 ·
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4

Undergrad What is the importance of p-Sylow subgroups in understanding group structure?

  • Santiago24
  • · Replies 2 ·
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2

Undergrad Generators of Galois group of ## X^n - \theta ##

  • kmitza
  • · Replies 3 ·
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3

High School Determinant of a transposed matrix

  • Eclair_de_XII
  • · Replies 3 ·
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3

Graduate How Does the Non-Equality of Kernels Imply Their Sum Equals the Vector Space?

  • Portuga
  • · Replies 2 ·
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2

Graduate Why does the skew symmetric matrix form give the cross product?

  • Trying2Learn
  • · Replies 14 ·
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14

Undergrad Factoring Matrices with Elementary Row Operations

  • cbarker1
  • · Replies 4 ·
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4

Graduate Calculating the Modal Matrix for A

  • boo
  • · Replies 9 ·
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9

Undergrad What Conditions Ensure the Minimal Polynomial of α Divides P in Galois Theory?

  • giulio_hep
  • · Replies 12 ·
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12

Graduate How to visualise complex vector spaces of dimension 2 and above

  • pellis
  • · Replies 4 ·
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4

Undergrad Basis of 2x2 matrices with real entries

  • LagrangeEuler
  • · Replies 11 ·
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11

Undergrad Proving properties of polynomial in K[x]

  • kmitza
  • · Replies 8 ·
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8

What Are the Possible Jordan Forms and Characteristic Polynomial of T?

  • darksidemath
  • · Replies 1 ·
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1

Undergrad How to find the generator of this Lie group?

  • Haorong Wu
  • · Replies 1 ·
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1

Group Elements of Z24: Find the Order

  • Yara Leonard
  • · Replies 2 ·
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2

When does a 4×4 linear system have at most 2 solutions?

  • bargaj
  • · Replies 1 ·
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1

-la.1.1.19 the augmented process

  • karush
  • · Replies 10 ·
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10

Undergrad Orthogonality of Eigenvectors of Linear Operator and its Adjoint

  • ughpleasenope
  • · Replies 3 ·
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3

Undergrad Does associativity imply bijectivity in group operations?

  • valenumr
  • · Replies 38 ·
2
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38

Graduate Tensor differentiation and positive semidefinite inequalities

  • pitaly
  • · Replies 5 ·
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5

3.13 Compute the orders of the following groups:

  • karush
  • · Replies 3 ·
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3
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8

307.8.3 Compute A^n for the Jordan block

  • karush
  • · Replies 7 ·
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7

311.3.1.1 - Determinants And Cofactor Expansion

  • karush
  • · Replies 3 ·
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3

What are the generators of $\Bbb{Z}_6, \Bbb{Z}_8,$ and $\Bbb{Z}_{20}$?

  • karush
  • · Replies 5 ·
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5

Set of vectors form a vector space

  • karush
  • · Replies 2 ·
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2

Describes elements of D_5 using SAGE

  • karush
  • · Replies 6 ·
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6
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4

Undergrad What is a dyadic and what are they used for?

  • Trying2Learn
  • · Replies 3 ·
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3

Undergrad Linear Algebra 1 problem, Vector Geometry: Lines

  • Student323
  • · Replies 3 ·
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3

Undergrad Is this basis valid for polynomials with p(0)=p(1)?

  • Hall
  • · Replies 39 ·
2
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39

Undergrad S is set of all vectors of form (x,y,z) such that x=y or x =z. Basis?

  • Hall
  • · Replies 5 ·
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5

High School Proof involving two linear equations

  • RM86Z
  • · Replies 17 ·
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17

Undergrad How can I find all possible Jordan forms?

  • laurabon
  • · Replies 8 ·
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8

How Do You Solve Linear Equations with Given Coordinates?

  • Sarahq
  • · Replies 2 ·
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2

Graduate What is the Definition and Properties of a Cross Product in Vector Algebra?

  • Greg Bernhardt
  • · Replies 3 ·
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3

Undergrad Looking for a creative or quick method for finding roots in GF(p^n)

  • kmitza
  • · Replies 3 ·
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3

Undergrad Similarity transformation, basis change and orthogonality

  • Azad Koshur
  • · Replies 20 ·
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20

Undergrad Irreducible polynomials and prime elements

  • darksidemath
  • · Replies 5 ·
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5

Graduate Will solving A*A'=B for A always give a unique matrix?

  • feynman1
  • · Replies 18 ·
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18

Solve System Using Matrix Inverse

  • brinlin
  • · Replies 2 ·
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2

Undergrad Why is musical isomorphism called musical?

  • lriuui0x0
  • · Replies 2 ·
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2

Undergrad Finding a polynomial that has solution (root) as the sum of roots

  • swampwiz
  • · Replies 13 ·
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13

Undergrad Why does every polynomial of degree n have exactly n roots in C?

  • Delta2
  • · Replies 43 ·
2
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43

What does delta*w(z, z) mean in this complex number proof?

  • Bat1
  • · Replies 4 ·
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4