Linear and Abstract Algebra Forum

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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.
High School Rotating a point in 3-space through an angle about some vector
  • Eclair_de_XII
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Graduate Algebraic proof that Euler angles define a proper rotation matrix
  • Trying2Learn
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Find Matrix A for System Ax=1, 3
  • evinda
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Graduate How do you invert a 3D matrix? (Tensor inversion)
  • BoltE
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Is the Condition Number of A'A Related to its Matrix Norm?
  • mathmari
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Undergrad Is G simple?Is G simple? A different approach using Sylow theorems
  • seanthinks
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Graduate Equivalence Relation to define the tensor product of Hilbert spaces
  • victorvmotti
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Undergrad Interpretation of "pseudo-diagonalisation"
  • jk22
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High School Understanding Dual Space: Mapping Vector Space to Real Numbers
  • geordief
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Undergrad Complex-Linear Matrices & C-Linear Transformations .... Tapp, Propn 2.4 ....
  • Math Amateur
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Linear Transformations & Matrices: Armstrong, Tapp Chs. 9 & 1 - Explained
  • Math Amateur
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Graduate Elementwise Derivative of a Matrix Exponential
  • madness
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Graduate Eigenvectors and matrix inner product
  • SeM
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Graduate Extending a linear representation by an anti-linear operator
  • hideelo
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Graduate Tensor symmetries and the symmetric groups
  • leo.
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Graduate Diagonalizing Hermitian matrices with adjoint representation
  • Luck0
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Undergrad Expressing the Matrix Transpose Function: Is There a Different Approach?
  • madness
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Undergrad Group Theory sub algebra of unitary group of U(6) group.
  • Vikas Katoch
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6
How Can I Use GeoGebra to Calculate Vector Lengths and Projections?
  • mathmari
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Undergrad Representing conversion of (1,1) tensor to (2,0) tensor
  • Shirish
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Determine the cycle decomposition of the permutations
  • mathmari
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Do disjoint cycles commute under exponentiation? (Curious)
  • mathmari
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Which is the geometric interpretation?
  • mathmari
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Finding a Vector Perpendicular to the Line of Reflection
  • mathmari
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Undergrad Proving functions are linearly dependent
  • brotherbobby
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Understanding Map Interpretation and Shadow Projection on a Plane
  • mathmari
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Calculating Determinants: Using Laplace Expansion or Echelon Form?
  • mathmari
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Undergrad The irreducible representations of of su(2): Highest weight method
  • Hydaspex
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Undergrad Properties of Defective Matrices in Space?
  • madness
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Determine the solution set of the system using the echelon form
  • mathmari
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Linear Maps in $\mathbb{R}^n$ and $\mathbb{R}^m$: Proving Properties with $M$
  • mathmari
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Undergrad Notation inquiry - bar over basis set....
  • berlinspeed
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Understanding Symmetry Maps and Rotations in the Plane
  • mathmari
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Rotations, Reflections and Translations
  • mathmari
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Define matrix to get a row operation of type 1
  • mathmari
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The permutation induces on the set
  • mathmari
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Graduate Question about the irreducible representation of a rank 2 tensor under SO(3)
  • TroyElliott
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How to Solve a Linear Equation System Using Row Reduction?
  • karush
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Undergrad Linear Isomorphisms: Understand & Apply
  • Lauren1234
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Undergrad Proving Linear Transformation of V with sin(x),cos(x) & ex
  • Lauren1234
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Graduate Decomposing SU(4) into SU(3) x U(1)
  • RicardoMP
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Solving a Matrix Problem on IGCSE Past Paper: Part B
  • Funfinder15
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Is $\phi(U)$ a Subspace of $\mathbb{R}^m$?
  • mathmari
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Possible mistake in question? (system of linear inequalities)
  • swag312
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Undergrad Understanding the Derivation of Reciprocal Lattice Basis from Equations 5 and 6
  • sam45
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Graduate Representations of finite groups -- Equivalent representations
  • LagrangeEuler
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Graduate Representations of finite groups: Irreducible and reducible
  • LagrangeEuler
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Graduate Difference Between Subgroup & Closed Subgroup of a Group
  • LagrangeEuler
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High School What Does Skew Symmetry Imply for One-Dimensional Systems?
  • hoddy
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Undergrad Rational functions in one indeterminate - useful concept?
  • Stephen Tashi
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Undergrad 2 and 3 dimensional invariant subspaces of R4
  • nigelscott
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Decide if the sets are subspaces or affine subspaces
  • mathmari
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Proving $\{w_1, \ldots , w_m\}$ is a Basis of $\text{Lin}(v_1, \ldots , v_k)$
  • mathmari
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How Does the Determinant of a Matrix Relate to the Area of a Parallelogram?
  • mathmari
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High School Need an Equation for converting Vertical to horizontal FOV
  • Justice Hunter
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Undergrad How Can I Improve My Method for Translating Points on Coordinate Axes?
  • RichardWattUK
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Relationship between three planes
  • mathmari
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Norms for a Linear Transformation .... Browder, Lemma 8.4 ....
  • Math Amateur
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Undergrad Math for Blending Numbers: Find "X
  • fifthFunction
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4
Understanding Browder's Remarks on Linear Transformations
  • Math Amateur
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Proving Linear Dependence and Span in n-dimensional Space
  • mathmari
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Are the vectors linearly independent?
  • mathmari
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Undergrad Condition for a pair of straight lines
  • rajeshmarndi
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Graduate Is There a Closed Form for Airy Disk Eigenfunctions?
  • marcusl
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High School I am 47 years old and I trying to learn Mathematics
  • Marcio reis
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High School Does This Equation Hold in All Commutative Rings?
  • donglepuss
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Subset that satisfies all but one axioms of subspaces
  • mathmari
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What is the intersection of two spans?
  • mathmari
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Graduate Solvability Of The Couniversal Mapping Problem On Products
  • fresh_42
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Undergrad Issue with perspective projection?
  • Huyanyinglei
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Can These Mathematical Sets Be Considered Subspaces?
  • mathmari
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[ASK] Determinant of a Matrix with Polynomial Elements
  • Monoxdifly
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Graduate Understanding Induced Maps: Types and Applications
  • WWGD
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Undergrad Meaning of mapping R[X]->Maps[R,R]
  • spacetimedude
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Concatenating Lists: Associative but Not Commutative/Idempotent
  • Kenan1
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Prove the statements : Vectors/Matrices
  • mathmari
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High School Matrix Exponential: Researching Origins & Applications
  • lekh2003
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What are the properties of distance?
  • mathmari
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Undergrad Radial Vector in Cartesian form
  • Arman777
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Undergrad Find the minimum and maximum value of a quadratic form
  • schniefen
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Undergrad Find matrix of linear transformation and show it's diagonalizable
  • schniefen
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Short topical webpage title: Proving Properties of Unital Rings
  • fredpeterson57
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Undergrad Generalisation of Polarization identity
  • Geometry
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Graduate Solutions of Matrix Equation A X B^T = C
  • quark002
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Undergrad Show isometry and find geometric meaning
  • schniefen
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Undergrad The essence of the eigen problem
  • Carbon273
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Undergrad General equation for the magnitude of the difference vector
  • jonander
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15
Undergrad Is the Projection Matrix A^2=A Valid in R^4?
  • schniefen
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Undergrad Proof of ##F## is an orthogonal projection if and only if symmetric
  • schniefen
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4 problems regarding automorphisms/homomorphisms
  • AutGuy98
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Undergrad Intersection of a plane with a segment in n dimensions
  • jk22
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Undergrad Prove that F^infinity is infinite dimensional
  • nox
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Undergrad Why Does a Rank One Matrix with a=1 Still Have Solutions?
  • Carbon273
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High School Why is sine not used for dot product?
  • Kirkkh
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Undergrad Tensor calculation, giving|cos A|>1: how to interpret
  • nomadreid
  • · Replies 13 ·
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Undergrad Why Use Nonlinear Polynomials for Linearization?
  • MikeSv
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Undergrad Proving a formula for special determinants
  • schniefen
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Undergrad Projectile angle (straight line) between 2 planets
  • thomasvt
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Graduate Performing MLEM with Response Matrix for 4pi Imager and 1x3 Vector Input
  • a.glick
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List all the subgroups H of C_(12)
  • AutGuy98
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