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

Construct a matrix with such that V is not equal to C_x

  • catsarebad
  • · Replies 5 ·
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5

Undergrad How Do Unit Vectors Achieve Their Form?

  • JasonHathaway
  • · Replies 9 ·
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9

Show deg of minimal poly = dimension of V

  • catsarebad
  • · Replies 1 ·
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1

Tensor Products - Keith Conrad - Theorem 3.3 - Tensor Products I

  • Math Amateur
  • · Replies 3 ·
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3

Polynomial including Sigma Notation

  • PurpleDude
  • · Replies 4 ·
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4

Graduate Calculating Basis of Tangent Plane

  • flyinjoe
  • · Replies 2 ·
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2

Existence of Tensor Products - Keith Conrad - Tensor Products I - Theorem 3.2

  • Math Amateur
  • · Replies 7 ·
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7

Graduate Generating randomly oriented non-intersecting cylinders in a unit cell

  • tricha122
  • · Replies 9 ·
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9

Graduate Is this matrix exponentiation method correct?

  • Jhenrique
  • · Replies 2 ·
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2

Group Isomorphism: Proving G Is an Odd, Ablian Group

  • Andrei1
  • · Replies 2 ·
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2

Difference Between Lines and Vectors (Linear Combination Problem)

  • esis
  • · Replies 7 ·
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7

High School Why is a/(as+1) equivalent to 1/(s+1/a)?

  • tranceical
  • · Replies 5 ·
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5

Polynomial that includes complex numbers

  • PurpleDude
  • · Replies 16 ·
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16

What Are the Subgroups of Z_n When n Is Even?

  • alyafey22
  • · Replies 3 ·
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3

Is the image of a direct sum equal to the union of images?

  • Fermat1
  • · Replies 1 ·
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1

Graduate How do you solve a system of equations with 4 variables and 4 equations?

  • noowutah
  • · Replies 6 ·
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6

Graduate Why f(x) = x^n - r e^{i \theta}? Seeking Analytic Explanation

  • ggb123
  • · Replies 2 ·
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2

Set of eigenvectors is linearly independent

  • Fermat1
  • · Replies 1 ·
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1

Graduate Why do number theorists prefer elementary proofs?

  • James MC
  • · Replies 8 ·
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8

Graduate How Does the Adjoint Map Function in Lie Theory?

  • Mandelbroth
  • · Replies 3 ·
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3

3 Algebra problems that I with.

  • namerequired
  • · Replies 4 ·
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4

Introduction to Tensor Products - some advice please

  • Math Amateur
  • · Replies 3 ·
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3

Algorithm for finding all the borders of R in all dimensions?

  • esis
  • · Replies 4 ·
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4

Undergrad How Do You Sketch Re(iz) = 3 in Complex Number Plane?

  • JC3187
  • · Replies 5 ·
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5

Simple problem concerning R[x], R and a prime ideal I

  • Math Amateur
  • · Replies 4 ·
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4

Graduate New irrational number to develop transcendental operators

  • clairaut
  • · Replies 2 ·
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2

Show that the matrix D is invertible

  • mathmari
  • · Replies 4 ·
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4

Graduate Maximizing resultant magnitude by flipping 2D vectors

  • Jeff.Nevington
  • · Replies 2 ·
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2

Proving ^eI = D^-1R iff I ∩ D ≠ ∅ in localization

  • Math Amateur
  • · Replies 9 ·
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9

Group of polynomials with coefficients from Z_10.

  • alyafey22
  • · Replies 14 ·
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14

Solving a Matrix Equation: Choosing the Right Answer

  • Yankel
  • · Replies 7 ·
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7

Are W and V subspaces of their parent vector spaces?

  • Yankel
  • · Replies 1 ·
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1

Graduate Newton's expansion for non-commutative quantities

  • ShayanJ
  • · Replies 2 ·
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2

Undergrad Vector Formula with multiple Equal signs?

  • TastyLemons
  • · Replies 2 ·
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2

Which of the Following is Incorrect Regarding Matrices and Vectors?

  • Yankel
  • · Replies 2 ·
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2

Graduate Approximate diagonalisation of (3,3) hermitian matrix

  • SUSY
  • · Replies 2 ·
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2

Localization - Bijections between prime ideals of R and D^-1R

  • Math Amateur
  • · Replies 1 ·
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1
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1

Graduate Fully reducible rep-invariant subspace

  • ChrisVer
  • · Replies 1 ·
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1

Positive, definite matrix symmetric

  • kalish1
  • · Replies 1 ·
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1

Undergrad Understanding Solutions and Singular Matrices

  • Plasmarobo
  • · Replies 9 ·
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9

Graduate Pythagorean theorem based on cross product.

  • tony700
  • · Replies 3 ·
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3

Free and Finitely Generated Modules

  • Sudharaka
  • · Replies 1 ·
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1

Graduate Inner products and the dual space

  • orion
  • · Replies 20 ·
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20

Collection of Subspaces of a Vector Space

  • Sudharaka
  • · Replies 4 ·
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4
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1

Graduate Infinity and one norm question

  • Visceral
  • · Replies 3 ·
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3

Undergrad Understanding Linear Combinations of Vectors

  • Bashyboy
  • · Replies 2 ·
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2

Graduate How Does Matrix Exponentiation Retrieve Rotation Matrices?

  • gentsagree
  • · Replies 3 ·
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3

Undergrad When y is negative in linear regression?

  • xeon123
  • · Replies 4 ·
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4

Undergrad Algorithm for Generating Percentage Amounts

  • natedgreat3
  • · Replies 5 ·
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5

Graduate What is com(M) for a matrix and what are its properties?

  • Jhenrique
  • · Replies 3 ·
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3

Quick problem: given the slope and a point, find the line

  • tmt1
  • · Replies 2 ·
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2
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7

R-modules and Homomorphism of Rings

  • Sudharaka
  • · Replies 3 ·
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3

Localization - Dummit and Foote, EXAMPLE 2, Ch. 15, Section 15.4, page 708

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad How can you manipulate a vector to create different matrices?

  • Jhenrique
  • · Replies 5 ·
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5

Graduate Rotation Equations for 2 Angles: Combining Relationships for Easy Calculation

  • Jhenrique
  • · Replies 2 ·
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2

Graduate Anthropomorphic Dummy Movements in 3D Space

  • PrinceAlee
  • · Replies 4 ·
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4

Graduate Transforming a spatial average into a spectral average

  • nickthequick
  • · Replies 2 ·
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2

Undergrad Consistency of A System of Linear Equations

  • Bashyboy
  • · Replies 1 ·
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1

Localization in Commutative Ring Theory

  • Math Amateur
  • · Replies 16 ·
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16

Graduate Scalar, vector and tensor calculus

  • Jhenrique
  • · Replies 2 ·
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2

If a row is added to any matrix is it still the same matrix?

  • find_the_fun
  • · Replies 4 ·
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4

Find Unit Vector Orthogonal to Vector

  • annie122
  • · Replies 4 ·
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4

Graduate Can isomorphic subfields of a field be different?

  • Mandelbroth
  • · Replies 1 ·
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1

Graduate What is the significance of the basis vector e_{11} in a bivector?

  • Jhenrique
  • · Replies 3 ·
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3

Graduate How can I find a x such that the order of 2 mod x is n?

  • stroustroup
  • · Replies 2 ·
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2

Graduate Eigenvalues of two matrices are equal

  • gopi9
  • · Replies 18 ·
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18

Graduate Covariant and Contravariant Coordinate

  • Jhenrique
  • · Replies 1 ·
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1

Find Vectors $\vec{v_1}$, $\vec{v_2}$, $\vec{v_3}$ Given Dot Products

  • Saitama
  • · Replies 4 ·
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4

Graduate Changing bases (with bra-ket notation)

  • iScience
  • · Replies 3 ·
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3

Graduate How Does Tikhonov Regularization Handle Underflows in IEEE Double Precision?

  • vibe3
  • · Replies 1 ·
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1

Linear Function on a Vector Space

  • Sudharaka
  • · Replies 7 ·
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7

Self Adjoint and Unitary Transformations

  • Sudharaka
  • · Replies 2 ·
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2

Graduate Why Is U(n) Considered Connected When O(n) Is Not?

  • gentsagree
  • · Replies 3 ·
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3

Why Is There No Division for Vectors?

  • find_the_fun
  • · Replies 4 ·
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4

How to compute P'(1-x) for a linear map from P₃ to P₂

  • Petrus
  • · Replies 3 ·
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3

High School Cross product between unit vectos

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Finding the Intersection of a Line and Plane

  • pandalolwut
  • · Replies 1 ·
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1

Undergrad Why no general solution to quintic equations?

  • Superhoben
  • · Replies 5 ·
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5

Extend to an orthonormal basis for R^3

  • Petrus
  • · Replies 4 ·
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4

Graduate Rotational in terms of vector calculus

  • Jhenrique
  • · Replies 1 ·
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1

What Is the Relationship Between Radicals and Prime Ideals?

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Curl and divergence of units vectos

  • Jhenrique
  • · Replies 2 ·
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2

What Are Linear Transformations and How Do They Work?

  • Petrus
  • · Replies 2 ·
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2

How can I show that K is positive-definite?

  • evinda
  • · Replies 2 ·
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2

Cauchy-Schwarz inequality for pre-inner product

  • mozganutyj
  • · Replies 2 ·
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2

Jordan Normal Form of a Linear Transformation

  • Sudharaka
  • · Replies 23 ·
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23

Graduate Why do Laplacian and Hessian both use the same notation d²/dr²?

  • Jhenrique
  • · Replies 2 ·
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2

Basis, dimension and vector spaces

  • Yankel
  • · Replies 5 ·
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5

Non-Singular Bilinear Function

  • Sudharaka
  • · Replies 3 ·
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3

Is the Space of Real Polynomials of Degree ≤ n a Euclidean Space?

  • Sudharaka
  • · Replies 3 ·
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3

Is the Lower Triangular Matrix in the Cholesky Decomposition Unique?

  • evinda
  • · Replies 11 ·
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11

Graduate Vector components and its coordinate description in a given basis

  • "Don't panic!"
  • · Replies 6 ·
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6

Ideals of a Residue Class Ring- Ring Isomorphism

  • Math Amateur
  • · Replies 2 ·
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2

Graduate When do subgroups of larger order avoid containing a normal subgroup?

  • epr1990
  • · Replies 1 ·
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1

Graduate Irreducible representation. I'm confused.

  • LagrangeEuler
  • · Replies 14 ·
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14

Graduate Applying linear transformations to orthonormal basis vectors

  • iScience
  • · Replies 1 ·
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1

Graduate Proving the special property of diagonal matrix?

  • Seydlitz
  • · Replies 3 ·
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3