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 Solving Eigenvalues: Complex Numbers Solutions

  • izzy93
  • · Replies 4 ·
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4

Graduate Why this paradox in calculating eigen values for T*T ?

  • vish_maths
  • · Replies 9 ·
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9

Undergrad Why Do Rank 1 Matrices Have Eigenvalues 0 and Trace?

  • brownman
  • · Replies 3 ·
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3

Undergrad Split a Matrix into and arbitrary number of blocks

  • DarkFalz
  • · Replies 3 ·
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3

What Does Reducing Z[x] Modulo the Prime Ideal (p) in Polynomial Rings Mean?

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Presentation of a group to generators in A(S)

  • TylerH
  • · Replies 1 ·
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1

Undergrad Solutions to Ax=b lie in row space?

  • engineer_ja
  • · Replies 6 ·
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6

Esteban's question at Yahoo Answers (Field extension)

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate Hilbert Space Interpretation of Fourier Transform

  • thegreenlaser
  • · Replies 16 ·
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16

Prime X 's question at Yahoo Answers (Eigenvalues of AB and BA)

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate Is the Dual Space a Subset of V?

  • MonicaRita
  • · Replies 12 ·
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12

Gregory's question at Yahoo Answers (Inner product space)

  • Fernando Revilla
  • · Replies 1 ·
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1

Undergrad Arctangent2 without square rooting?

  • sparkzbarca
  • · Replies 1 ·
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1

Graduate A three-gear alignment problem, simultaneous equations

  • bobsalive
  • · Replies 3 ·
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3

Integral Domains and Principal Ideal Domains (PIDs)

  • Math Amateur
  • · Replies 4 ·
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4

Proof of G Abelian When 3-abelian & 5-abelian

  • mathbalarka
  • · Replies 2 ·
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2

Undergrad How do I show that the vectors of an invertible MX are indepedent?

  • Minhtran1092
  • · Replies 4 ·
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4

Graduate Determinant Function: Understanding Orientation

  • Tenshou
  • · Replies 6 ·
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6

Graduate Isomorphism between groups and their Lie Algebra

  • raopeng
  • · Replies 4 ·
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4

Graduate Groups of order 12 whose 3-Sylow subgroups are not normal.

  • Artusartos
  • · Replies 1 ·
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1

Graduate How Does the Isomorphism Between Z_k and Aut(Z_n) Work?

  • Artusartos
  • · Replies 2 ·
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2

Graduate Elementary question about Dirac notation

  • Ocifer
  • · Replies 2 ·
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2

Graduate Any ideas for an explicit formula?

  • Someone2841
  • · Replies 1 ·
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1

Undergrad Finding the least square solution with only positive coefficients

  • Marvin_MKII
  • · Replies 4 ·
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4

High School Linear equations using addition

  • uperkurk
  • · Replies 7 ·
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7

Area of the parallelogram when diagonal vectors are given.

  • Suvadip
  • · Replies 2 ·
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2

Graduate Covariant and Contravariant Components of a Vector

  • LawdyLawdy
  • · Replies 4 ·
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4

Graduate Can't understand this statement about factor rings

  • Silversonic
  • · Replies 1 ·
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1

Integral closure in finite extension fields

  • pantboio
  • · Replies 1 ·
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1

Graduate How Can You Represent Determinants Using Permutations?

  • jtceleron
  • · Replies 1 ·
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1

Solving for Distinct Vectors of G: $\mathbb{F}_p$, n, and v

  • jakncoke1
  • · Replies 2 ·
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2

C.c.'s question at Yahoo Answers regarding factoring a polynomial

  • MarkFL
  • · Replies 1 ·
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1

A fundamental fact about Linear Algebra

  • caffeinemachine
  • · Replies 3 ·
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3

Graduate My Proof of Structure Theorem for Finite Abelian Groups

  • Site
  • · Replies 4 ·
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4

Proofs about invertible linear functions

  • i_a_n
  • · Replies 8 ·
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8

Principal Ideals - Need for a ring with identity or a unity

  • Math Amateur
  • · Replies 14 ·
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14

Graduate Proving Invertible Matrix Theorem: A^TDA=D

  • dEdt
  • · Replies 8 ·
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8

Principal ideal in a ring without identity

  • Math Amateur
  • · Replies 6 ·
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6

Is the Analysis of Principal Ideals Correct?

  • Math Amateur
  • · Replies 2 ·
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2

Find $\det(A+B)$ given $\det(A)=4$

  • Petrus
  • · Replies 9 ·
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9

Graduate Discrete or continuous spectrum?

  • ShayanJ
  • · Replies 1 ·
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1

Graduate Connection between topoi and schemes

  • Jim Kata
  • · Replies 1 ·
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1

Comaximal Ideals in a Principal Ideal Domain

  • Math Amateur
  • · Replies 3 ·
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3

Prime elements in integral domains

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Derive an expression to find how many times an eigen value is repeated

  • vish_maths
  • · Replies 9 ·
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9

Proving Commutativity of * on Set S

  • jakncoke1
  • · Replies 1 ·
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1

Proving that $S_1 \cdot S_2 \in S$

  • jakncoke1
  • · Replies 1 ·
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1

Graduate Showing V is the direct sum of W1 and W2

  • La_Lune
  • · Replies 1 ·
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1

Graduate Group Axiom Ordering: Proving Associativity First

  • bologna121121
  • · Replies 3 ·
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3

Gcd of polynomials is 1. There is an nxn matrix with determinant....

  • caffeinemachine
  • · Replies 5 ·
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5

Graduate Proof that Determinant is Multiplicative for Commutative Rings

  • Site
  • · Replies 4 ·
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4

Graduate Why Can Every Element of SO⁺(1,3) Be Expressed as an Exponential?

  • parton
  • · Replies 7 ·
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7
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1

Is the Inner Product Space in C[0,2] Satisfied by the Integral Equality?

  • Poirot1
  • · Replies 5 ·
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5

Graduate Geometric insight about rotations needed

  • Fredrik
  • · Replies 2 ·
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2

Undergrad Proving a Linear Transformation is Onto

  • BrainHurts
  • · Replies 8 ·
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8

Arjun's question at Yahoo Answers (Equivalence relation)

  • Fernando Revilla
  • · Replies 1 ·
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1

Undergrad General Proof of Cross/Dot Product

  • mathnerd15
  • · Replies 15 ·
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15

Graduate Finiding a representative of the 2nd conjugacy class in A_n

  • skojoian
  • · Replies 2 ·
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2

Graduate Difficult Number Theory question

  • kurtulmehtap
  • · Replies 12 ·
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12

Andrew's question at Yahoo Answers (Similar matrices)

  • Fernando Revilla
  • · Replies 1 ·
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1

Undergrad Scalars and determining subspaces

  • MoreDrinks
  • · Replies 2 ·
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2

Relation between Hermite and associated Laguerre

  • Suvadip
  • · Replies 1 ·
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1

Graduate Nth term of prime number sequence

  • scimad
  • · Replies 7 ·
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7

Graduate Nonlinear Operators on Finitely Generated Vector Spaces: Group Property Example

  • Zelyucha
  • · Replies 5 ·
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5

Is the Exponential of a Linear Operator Defined?

  • ryo0071
  • · Replies 5 ·
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5

Graduate Is Dirac Delta a Function or a Distribution?

  • ShayanJ
  • · Replies 4 ·
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4

Graduate When do SO(2) actions on the circle in the plane determine a metric?

  • lavinia
  • · Replies 1 ·
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1

Graduate Understanding Linear Perceptrons and their Decision Boundary in Neural Networks

  • 3.141592654
  • · Replies 1 ·
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1

Undergrad Vector image on another vector

  • baby_1
  • · Replies 6 ·
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6

Graduate Possible Matrix with Equal Row and Column Sums?

  • bb700092
  • · Replies 1 ·
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1

Graduate Global position and orientation of a point relative to another

  • helloearthling
  • · Replies 2 ·
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2

Undergrad How to solve a problem involving modulus

  • hackish
  • · Replies 2 ·
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2

Theman123's question at Yahoo Answers (Rotation and reflection)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Is the Product of Two Diagonalizable Matrices Always Diagonalizable?

  • Yankel
  • · Replies 2 ·
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2

Shelby's question at Yahoo Answers (Finding P with P^{-1}AP=D)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Graduate Sketch Conics: Motivating Students to Learn Cross Products

  • matqkks
  • · Replies 1 ·
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1

Sketch Conics: Motivating Students to Learn Cross Product Terms

  • matqkks
  • · Replies 2 ·
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2

Graduate What is the significance of free products in group theory?

  • dumbQuestion
  • · Replies 4 ·
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4

Undergrad Some questions about 3D environment

  • baby_1
  • · Replies 1 ·
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1

Use a subgroup lattice to compute a normalizer

  • i_a_n
  • · Replies 1 ·
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1

Identify isomorphism type for each proper subgroup of (Z/32Z)*

  • i_a_n
  • · Replies 37 ·
2
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37

Undergrad Factoring x^3+y^3+z^3: Conditions & Solutions

  • JNeutron2186
  • · Replies 2 ·
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2

Amanda's question at Yahoo Answers (Eigenvalues and eigenvectors)

  • Fernando Revilla
  • · Replies 1 ·
Replies
1

Graduate Determinant of product of matrices

  • LagrangeEuler
  • · Replies 1 ·
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1

Vector Triple Product: Simplification Possible?

  • Dustinsfl
  • · Replies 2 ·
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2

Does the permutation group S_8 contain elements of order 14?

  • i_a_n
  • · Replies 1 ·
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1

Graduate Why Denote Group Operation with Multiplication?

  • Site
  • · Replies 7 ·
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7

Comparing Matrices: A-B>0 Positive Definite?

  • matqkks
  • · Replies 4 ·
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4

Graduate Is There a Ring Homomorphism for All Unital Rings in Evaluation Homomorphism?

  • Monobrow
  • · Replies 4 ·
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4

Schreier's Lemma Proof not clear.

  • caffeinemachine
  • · Replies 2 ·
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2

Graduate Can A>B Be Determined by A-B>0 for Matrices?

  • matqkks
  • · Replies 1 ·
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1

How many possibly unique entries are there in a symmetric tensor?

  • ssh
  • · Replies 1 ·
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1

Graduate Combine two pitch, yaw, roll rotations

  • Ziks
  • · Replies 6 ·
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6

Can Rank of A Determine Rank of A+A²+A³+A⁴?

  • Suvadip
  • · Replies 1 ·
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1

Dale Simpson's question at Yahoo Answers (One-to-one matrix)

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate What Iterative Method is This?

  • Iseous
  • · Replies 15 ·
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15

Undergrad What does this answer mean? (continuous functions)

  • spaderdabomb
  • · Replies 1 ·
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1

Undergrad One-to-one linear transformations

  • Nikitin
  • · Replies 5 ·
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5

Undergrad Finding smallest solution to modular equations

  • Das Bot
  • · Replies 7 ·
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7