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 A Identical if A is a Square Matrix with Full Rank?

  • evinda
  • · Replies 6 ·
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6

Prove that CnXCm isomorphic to Cgcd(m,n)XClcm(m,n)

  • Alex224
  • · Replies 3 ·
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3

High School Rotating a point in 3-space through an angle about some vector

  • Eclair_de_XII
  • · Replies 2 ·
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2

Graduate Algebraic proof that Euler angles define a proper rotation matrix

  • Trying2Learn
  • · Replies 6 ·
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6

Find Matrix A for System Ax=1, 3

  • evinda
  • · Replies 12 ·
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12

Graduate How do you invert a 3D matrix? (Tensor inversion)

  • BoltE
  • · Replies 2 ·
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2

Is the Condition Number of A'A Related to its Matrix Norm?

  • mathmari
  • · Replies 3 ·
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3

Undergrad Is G simple?Is G simple? A different approach using Sylow theorems

  • seanthinks
  • · Replies 5 ·
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5

Graduate Equivalence Relation to define the tensor product of Hilbert spaces

  • victorvmotti
  • · Replies 1 ·
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1

Undergrad Interpretation of "pseudo-diagonalisation"

  • jk22
  • · Replies 5 ·
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5

High School Does the dual space always correspond one-to-one with the original vector space?

  • geordief
  • · Replies 48 ·
2
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48

Undergrad Proving C-linearity iff F(iX) = iF(X) in Tapp Prop 2.4

  • Math Amateur
  • · Replies 3 ·
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3

Why does Armstrong use the transpose in his linear transformation definition?

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Elementwise Derivative of a Matrix Exponential

  • madness
  • · Replies 2 ·
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2

Graduate Eigenvectors and matrix inner product

  • SeM
  • · Replies 1 ·
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1

Graduate Extending a linear representation by an anti-linear operator

  • hideelo
  • · Replies 1 ·
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1

Graduate Tensor symmetries and the symmetric groups

  • leo.
  • · Replies 1 ·
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1

Graduate Diagonalizing Hermitian matrices with adjoint representation

  • Luck0
  • · Replies 1 ·
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1

Undergrad Expressing the Matrix Transpose Function: Is There a Different Approach?

  • madness
  • · Replies 3 ·
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3

Undergrad Group Theory sub algebra of unitary group of U(6) group.

  • Vikas Katoch
  • · Replies 6 ·
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6

How Can I Use GeoGebra to Calculate Vector Lengths and Projections?

  • mathmari
  • · Replies 3 ·
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3

Undergrad Representing conversion of (1,1) tensor to (2,0) tensor

  • Shirish
  • · Replies 2 ·
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2

Determine the cycle decomposition of the permutations

  • mathmari
  • · Replies 28 ·
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28

Do disjoint cycles commute under exponentiation? (Curious)

  • mathmari
  • · Replies 5 ·
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5

Which is the geometric interpretation?

  • mathmari
  • · Replies 4 ·
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4

Proving σₓ is a linear isometry and finding a reflection vector

  • mathmari
  • · Replies 11 ·
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11

Undergrad Proving functions are linearly dependent

  • brotherbobby
  • · Replies 5 ·
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5

Understanding Map Interpretation and Shadow Projection on a Plane

  • mathmari
  • · Replies 19 ·
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19

Calculating Determinants: Using Laplace Expansion or Echelon Form?

  • mathmari
  • · Replies 13 ·
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13

Undergrad The irreducible representations of of su(2): Highest weight method

  • Hydaspex
  • · Replies 4 ·
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4

Undergrad Properties of Defective Matrices in Space?

  • madness
  • · Replies 8 ·
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8

Determine the solution set of the system using the echelon form

  • mathmari
  • · Replies 2 ·
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2

What is M in the properties M(φ+ψ) = M(φ)+M(ψ)?

  • mathmari
  • · Replies 10 ·
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10

Undergrad What does the bar notation over a basis set mean?

  • berlinspeed
  • · Replies 2 ·
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2

Understanding Symmetry Maps and Rotations in the Plane

  • mathmari
  • · Replies 17 ·
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17

Matrix of reflection and rotation with composition properties

  • mathmari
  • · Replies 4 ·
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4

Define matrix to get a row operation of type 1

  • mathmari
  • · Replies 2 ·
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2

The permutation induces on the set

  • mathmari
  • · Replies 23 ·
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23

Graduate Why are symmetric and antisymmetric parts irreducible under SO(3)?

  • TroyElliott
  • · Replies 5 ·
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5

How to Solve a Linear Equation System Using Row Reduction?

  • karush
  • · Replies 4 ·
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4

Undergrad How to approach problems on linear isomorphisms

  • Lauren1234
  • · Replies 8 ·
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8

Undergrad Is the derivative a linear transformation on span of exponentials and trig functions?

  • Lauren1234
  • · Replies 9 ·
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9

Graduate Decomposing SU(4) into SU(3) x U(1)

  • RicardoMP
  • · Replies 1 ·
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1

Solving a Matrix Problem on IGCSE Past Paper: Part B

  • Funfinder15
  • · Replies 1 ·
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1

Is $\phi(U)$ a Subspace of $\mathbb{R}^m$?

  • mathmari
  • · Replies 10 ·
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10

Possible mistake in question? (system of linear inequalities)

  • swag312
  • · Replies 1 ·
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1

Undergrad How are equations 7a, 7b, 7c derived from equations 5 and 6?

  • sam45
  • · Replies 4 ·
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4

Graduate Representations of finite groups -- Equivalent representations

  • LagrangeEuler
  • · Replies 6 ·
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6

Graduate Representations of finite groups: Irreducible and reducible

  • LagrangeEuler
  • · Replies 1 ·
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1

Graduate What is the difference between a subgroup and a closed subgroup?

  • LagrangeEuler
  • · Replies 14 ·
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14

High School What Does Skew Symmetry Imply for One-Dimensional Systems?

  • hoddy
  • · Replies 3 ·
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3

Undergrad Rational functions in one indeterminate - useful concept?

  • Stephen Tashi
  • · Replies 31 ·
2
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31

Undergrad 2 and 3 dimensional invariant subspaces of R4

  • nigelscott
  • · Replies 1 ·
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1

Decide if the sets are subspaces or affine subspaces

  • mathmari
  • · Replies 3 ·
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3
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3
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15

High School Need an Equation for converting Vertical to horizontal FOV

  • Justice Hunter
  • · Replies 6 ·
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6

Undergrad How Can I Improve My Method for Translating Points on Coordinate Axes?

  • RichardWattUK
  • · Replies 2 ·
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2

Relationship between three planes

  • mathmari
  • · Replies 5 ·
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5

Browder Lemma 8.4: proving norm inequality for linear transformation

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Math for Blending Numbers: Find "X

  • fifthFunction
  • · Replies 4 ·
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4

Understanding Browder's Remarks on Linear Transformations

  • Math Amateur
  • · Replies 2 ·
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2

Proving Linear Dependence and Span in n-dimensional Space

  • mathmari
  • · Replies 3 ·
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3

Are the vectors linearly independent?

  • mathmari
  • · Replies 8 ·
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8

Undergrad Condition for a pair of straight lines

  • rajeshmarndi
  • · Replies 1 ·
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1

Graduate Is There a Closed Form for Airy Disk Eigenfunctions?

  • marcusl
  • · Replies 1 ·
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1

High School I am 47 years old and I trying to learn Mathematics

  • Marcio reis
  • · Replies 13 ·
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13

High School Does This Equation Hold in All Commutative Rings?

  • donglepuss
  • · Replies 5 ·
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5

Subset that satisfies all but one axioms of subspaces

  • mathmari
  • · Replies 16 ·
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16

What is the intersection of two spans?

  • mathmari
  • · Replies 8 ·
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8

Graduate Solvability Of The Couniversal Mapping Problem On Products

  • fresh_42
  • · Replies 13 ·
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13

Undergrad Issue with perspective projection?

  • Huyanyinglei
  • · Replies 5 ·
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5

Can These Mathematical Sets Be Considered Subspaces?

  • mathmari
  • · Replies 1 ·
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1

[ASK] Determinant of a Matrix with Polynomial Elements

  • Monoxdifly
  • · Replies 2 ·
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2

Graduate Understanding Induced Maps: Types and Applications

  • WWGD
  • · Replies 5 ·
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5

Undergrad Meaning of mapping R[X]->Maps[R,R]

  • spacetimedude
  • · Replies 9 ·
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9

Concatenating Lists: Associative but Not Commutative/Idempotent

  • Kenan1
  • · Replies 1 ·
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1

Proving properties of vector addition and 2×2 matrix multiplication

  • mathmari
  • · Replies 5 ·
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5

High School Origins of the matrix exponential in mathematics

  • lekh2003
  • · Replies 5 ·
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5

What are the properties of distance?

  • mathmari
  • · Replies 10 ·
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10

Undergrad Radial Vector in Cartesian form

  • Arman777
  • · Replies 8 ·
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8

Undergrad Find the minimum and maximum value of a quadratic form

  • schniefen
  • · Replies 8 ·
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8

Undergrad Find matrix of linear transformation and show it's diagonalizable

  • schniefen
  • · Replies 2 ·
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2

Short topical webpage title: Proving Properties of Unital Rings

  • fredpeterson57
  • · Replies 1 ·
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1

Undergrad Generalisation of Polarization identity

  • Geometry
  • · Replies 3 ·
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3

Graduate Solutions of Matrix Equation A X B^T = C

  • quark002
  • · Replies 1 ·
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1

Undergrad Show isometry and find geometric meaning

  • schniefen
  • · Replies 3 ·
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3

Undergrad The essence of the eigen problem

  • Carbon273
  • · Replies 17 ·
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17

Undergrad General equation for the magnitude of the difference vector

  • jonander
  • · Replies 15 ·
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15

Undergrad Is the Projection Matrix A^2=A Valid in R^4?

  • schniefen
  • · Replies 10 ·
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10

Undergrad Proof of ##F## is an orthogonal projection if and only if symmetric

  • schniefen
  • · Replies 3 ·
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3

4 problems regarding automorphisms/homomorphisms

  • AutGuy98
  • · Replies 5 ·
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5

Undergrad Intersection of a plane with a segment in n dimensions

  • jk22
  • · Replies 17 ·
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17

Undergrad Prove that F^infinity is infinite dimensional

  • nox
  • · Replies 26 ·
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26

Undergrad Why Does a Rank One Matrix with a=1 Still Have Solutions?

  • Carbon273
  • · Replies 5 ·
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5

High School Why is sine not used for dot product?

  • Kirkkh
  • · Replies 4 ·
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4

Undergrad Why does the angle between vectors in Minkowski space give |cos A|>1?

  • nomadreid
  • · Replies 13 ·
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13

Undergrad Why Use Nonlinear Polynomials for Linearization?

  • MikeSv
  • · Replies 10 ·
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10

Undergrad Proving a formula for special determinants

  • schniefen
  • · Replies 12 ·
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12

Undergrad Projectile angle (straight line) between 2 planets

  • thomasvt
  • · Replies 1 ·
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1