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 ·
Prove that CnXCm isomorphic to Cgcd(m,n)XClcm(m,n)
- Alex224
- · Replies 3 ·
High School Rotating a point in 3-space through an angle about some vector
- Eclair_de_XII
- · Replies 2 ·
Graduate Algebraic proof that Euler angles define a proper rotation matrix
- Trying2Learn
- · Replies 6 ·
Find Matrix A for System Ax=1, 3
- evinda
- · Replies 12 ·
Graduate How do you invert a 3D matrix? (Tensor inversion)
- BoltE
- · Replies 2 ·
Is the Condition Number of A'A Related to its Matrix Norm?
- mathmari
- · Replies 3 ·
Undergrad Is G simple?Is G simple? A different approach using Sylow theorems
- seanthinks
- · Replies 5 ·
Graduate Equivalence Relation to define the tensor product of Hilbert spaces
- victorvmotti
- · Replies 1 ·
Undergrad Interpretation of "pseudo-diagonalisation"
- jk22
- · Replies 5 ·
High School Does the dual space always correspond one-to-one with the original vector space?
- geordief
- · Replies 48 ·
Undergrad Proving C-linearity iff F(iX) = iF(X) in Tapp Prop 2.4
- Math Amateur
- · Replies 3 ·
Why does Armstrong use the transpose in his linear transformation definition?
- Math Amateur
- · Replies 2 ·
Graduate Elementwise Derivative of a Matrix Exponential
- madness
- · Replies 2 ·
Graduate Eigenvectors and matrix inner product
- SeM
- · Replies 1 ·
Graduate Extending a linear representation by an anti-linear operator
- hideelo
- · Replies 1 ·
Graduate Tensor symmetries and the symmetric groups
- leo.
- · Replies 1 ·
Graduate Diagonalizing Hermitian matrices with adjoint representation
- Luck0
- · Replies 1 ·
Undergrad Expressing the Matrix Transpose Function: Is There a Different Approach?
- madness
- · Replies 3 ·
Undergrad Group Theory sub algebra of unitary group of U(6) group.
- Vikas Katoch
- · Replies 6 ·
How Can I Use GeoGebra to Calculate Vector Lengths and Projections?
- mathmari
- · Replies 3 ·
Undergrad Representing conversion of (1,1) tensor to (2,0) tensor
- Shirish
- · Replies 2 ·
Determine the cycle decomposition of the permutations
- mathmari
- · Replies 28 ·
Do disjoint cycles commute under exponentiation? (Curious)
- mathmari
- · Replies 5 ·
Which is the geometric interpretation?
- mathmari
- · Replies 4 ·
Proving σₓ is a linear isometry and finding a reflection vector
- mathmari
- · Replies 11 ·
Undergrad Proving functions are linearly dependent
- brotherbobby
- · Replies 5 ·
Understanding Map Interpretation and Shadow Projection on a Plane
- mathmari
- · Replies 19 ·
Calculating Determinants: Using Laplace Expansion or Echelon Form?
- mathmari
- · Replies 13 ·
Undergrad The irreducible representations of of su(2): Highest weight method
- Hydaspex
- · Replies 4 ·
Undergrad Properties of Defective Matrices in Space?
- madness
- · Replies 8 ·
Determine the solution set of the system using the echelon form
- mathmari
- · Replies 2 ·
What is M in the properties M(φ+ψ) = M(φ)+M(ψ)?
- mathmari
- · Replies 10 ·
Undergrad What does the bar notation over a basis set mean?
- berlinspeed
- · Replies 2 ·
Understanding Symmetry Maps and Rotations in the Plane
- mathmari
- · Replies 17 ·
Matrix of reflection and rotation with composition properties
- mathmari
- · Replies 4 ·
Define matrix to get a row operation of type 1
- mathmari
- · Replies 2 ·
The permutation induces on the set
- mathmari
- · Replies 23 ·
Graduate Why are symmetric and antisymmetric parts irreducible under SO(3)?
- TroyElliott
- · Replies 5 ·
How to Solve a Linear Equation System Using Row Reduction?
- karush
- · Replies 4 ·
Undergrad How to approach problems on linear isomorphisms
- Lauren1234
- · Replies 8 ·
Undergrad Is the derivative a linear transformation on span of exponentials and trig functions?
- Lauren1234
- · Replies 9 ·
Graduate Decomposing SU(4) into SU(3) x U(1)
- RicardoMP
- · Replies 1 ·
Solving a Matrix Problem on IGCSE Past Paper: Part B
- Funfinder15
- · Replies 1 ·
Is $\phi(U)$ a Subspace of $\mathbb{R}^m$?
- mathmari
- · Replies 10 ·
Possible mistake in question? (system of linear inequalities)
- swag312
- · Replies 1 ·
Undergrad How are equations 7a, 7b, 7c derived from equations 5 and 6?
- sam45
- · Replies 4 ·
Graduate Representations of finite groups -- Equivalent representations
- LagrangeEuler
- · Replies 6 ·
Graduate Representations of finite groups: Irreducible and reducible
- LagrangeEuler
- · Replies 1 ·
Graduate What is the difference between a subgroup and a closed subgroup?
- LagrangeEuler
- · Replies 14 ·
High School What Does Skew Symmetry Imply for One-Dimensional Systems?
- hoddy
- · Replies 3 ·
Undergrad Rational functions in one indeterminate - useful concept?
- Stephen Tashi
- · Replies 31 ·
Undergrad 2 and 3 dimensional invariant subspaces of R4
- nigelscott
- · Replies 1 ·
Decide if the sets are subspaces or affine subspaces
- mathmari
- · Replies 3 ·
Proving $\{w_1, \ldots , w_m\}$ is a Basis of $\text{Lin}(v_1, \ldots , v_k)$
- mathmari
- · Replies 3 ·
How Does the Determinant of a Matrix Relate to the Area of a Parallelogram?
- mathmari
- · Replies 15 ·
High School Need an Equation for converting Vertical to horizontal FOV
- Justice Hunter
- · Replies 6 ·
Undergrad How Can I Improve My Method for Translating Points on Coordinate Axes?
- RichardWattUK
- · Replies 2 ·
Relationship between three planes
- mathmari
- · Replies 5 ·
Browder Lemma 8.4: proving norm inequality for linear transformation
- Math Amateur
- · Replies 1 ·
Undergrad Math for Blending Numbers: Find "X
- fifthFunction
- · Replies 4 ·
Understanding Browder's Remarks on Linear Transformations
- Math Amateur
- · Replies 2 ·
Proving Linear Dependence and Span in n-dimensional Space
- mathmari
- · Replies 3 ·
Are the vectors linearly independent?
- mathmari
- · Replies 8 ·
Undergrad Condition for a pair of straight lines
- rajeshmarndi
- · Replies 1 ·
Graduate Is There a Closed Form for Airy Disk Eigenfunctions?
- marcusl
- · Replies 1 ·
High School I am 47 years old and I trying to learn Mathematics
- Marcio reis
- · Replies 13 ·
High School Does This Equation Hold in All Commutative Rings?
- donglepuss
- · Replies 5 ·
Subset that satisfies all but one axioms of subspaces
- mathmari
- · Replies 16 ·
What is the intersection of two spans?
- mathmari
- · Replies 8 ·
Graduate Solvability Of The Couniversal Mapping Problem On Products
- fresh_42
- · Replies 13 ·
Undergrad Issue with perspective projection?
- Huyanyinglei
- · Replies 5 ·
Can These Mathematical Sets Be Considered Subspaces?
- mathmari
- · Replies 1 ·
[ASK] Determinant of a Matrix with Polynomial Elements
- Monoxdifly
- · Replies 2 ·
Graduate Understanding Induced Maps: Types and Applications
- WWGD
- · Replies 5 ·
Undergrad Meaning of mapping R[X]->Maps[R,R]
- spacetimedude
- · Replies 9 ·
Concatenating Lists: Associative but Not Commutative/Idempotent
- Kenan1
- · Replies 1 ·
Proving properties of vector addition and 2×2 matrix multiplication
- mathmari
- · Replies 5 ·
High School Origins of the matrix exponential in mathematics
- lekh2003
- · Replies 5 ·
What are the properties of distance?
- mathmari
- · Replies 10 ·
Undergrad Radial Vector in Cartesian form
- Arman777
- · Replies 8 ·
Undergrad Find the minimum and maximum value of a quadratic form
- schniefen
- · Replies 8 ·
Undergrad Find matrix of linear transformation and show it's diagonalizable
- schniefen
- · Replies 2 ·
Short topical webpage title: Proving Properties of Unital Rings
- fredpeterson57
- · Replies 1 ·
Undergrad Generalisation of Polarization identity
- Geometry
- · Replies 3 ·
Graduate Solutions of Matrix Equation A X B^T = C
- quark002
- · Replies 1 ·
Undergrad Show isometry and find geometric meaning
- schniefen
- · Replies 3 ·
Undergrad The essence of the eigen problem
- Carbon273
- · Replies 17 ·
Undergrad General equation for the magnitude of the difference vector
- jonander
- · Replies 15 ·
Undergrad Is the Projection Matrix A^2=A Valid in R^4?
- schniefen
- · Replies 10 ·
Undergrad Proof of ##F## is an orthogonal projection if and only if symmetric
- schniefen
- · Replies 3 ·
4 problems regarding automorphisms/homomorphisms
- AutGuy98
- · Replies 5 ·
Undergrad Intersection of a plane with a segment in n dimensions
- jk22
- · Replies 17 ·
Undergrad Prove that F^infinity is infinite dimensional
- nox
- · Replies 26 ·
Undergrad Why Does a Rank One Matrix with a=1 Still Have Solutions?
- Carbon273
- · Replies 5 ·
High School Why is sine not used for dot product?
- Kirkkh
- · Replies 4 ·
Undergrad Why does the angle between vectors in Minkowski space give |cos A|>1?
- nomadreid
- · Replies 13 ·
Undergrad Why Use Nonlinear Polynomials for Linearization?
- MikeSv
- · Replies 10 ·
Undergrad Proving a formula for special determinants
- schniefen
- · Replies 12 ·
Undergrad Projectile angle (straight line) between 2 planets
- thomasvt
- · Replies 1 ·