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.
MHB Test for compatibility of equations - Determinant |A b|
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MHB Show that there are vectors to get a basis
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MHB Kernel of Linear Map: Show $\ker \phi$ Equation
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Undergrad Proving Convexity of the Set X = {(x, y) E R^2; ax + by <= c} in R^2
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Undergrad The Paradox of u=v | Solve the Mystery
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MHB Is $2 + 8\sqrt{-5}$ a Unit or Irreducible in $\mathbb{Z} + \mathbb{Z}\sqrt{-5}$?
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Undergrad Logarithmic terms in a system of equations
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Undergrad Given two linear transformations L and K, show ##K = \lambda L## holds
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Undergrad Find the parameter values that make ##L## surjective
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MHB Method of least square: initial position & velocity
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MHB Projection Matrix Calculation for Vectors a_k: P_6P_5P_4P_3P_2P_1a_0
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MHB System no/infinitely many solution(s)
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MHB Is A Identical if A is a Square Matrix with Full Rank?
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MHB Prove that CnXCm isomorphic to Cgcd(m,n)XClcm(m,n)
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High School Rotating a point in 3-space through an angle about some vector
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Graduate Algebraic proof that Euler angles define a proper rotation matrix
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MHB Find Matrix A for System Ax=1, 3
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How do you invert a 3D matrix? (Tensor inversion)
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Undergrad Is G simple?Is G simple? A different approach using Sylow theorems
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Graduate Equivalence Relation to define the tensor product of Hilbert spaces
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Undergrad Interpretation of "pseudo-diagonalisation"
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High School Understanding Dual Space: Mapping Vector Space to Real Numbers
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Undergrad Complex-Linear Matrices & C-Linear Transformations .... Tapp, Propn 2.4 ....
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MHB Linear Transformations & Matrices: Armstrong, Tapp Chs. 9 & 1 - Explained
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Graduate Elementwise Derivative of a Matrix Exponential
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Graduate Eigenvectors and matrix inner product
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Graduate Extending a linear representation by an anti-linear operator
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Graduate Tensor symmetries and the symmetric groups
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Graduate Diagonalizing Hermitian matrices with adjoint representation
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Undergrad Expressing the Matrix Transpose Function: Is There a Different Approach?
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Undergrad Group Theory sub algebra of unitary group of U(6) group.
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MHB How Can I Use GeoGebra to Calculate Vector Lengths and Projections?
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Undergrad Representing conversion of (1,1) tensor to (2,0) tensor
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MHB Determine the cycle decomposition of the permutations
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MHB Do disjoint cycles commute under exponentiation? (Curious)
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MHB Which is the geometric interpretation?
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MHB Finding a Vector Perpendicular to the Line of Reflection
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Undergrad Proving functions are linearly dependent
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MHB Understanding Map Interpretation and Shadow Projection on a Plane
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MHB Calculating Determinants: Using Laplace Expansion or Echelon Form?
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Undergrad The irreducible representations of of su(2): Highest weight method
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Undergrad Properties of Defective Matrices in Space?
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MHB Determine the solution set of the system using the echelon form
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MHB Linear Maps in $\mathbb{R}^n$ and $\mathbb{R}^m$: Proving Properties with $M$
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Undergrad Notation inquiry - bar over basis set....
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MHB Understanding Symmetry Maps and Rotations in the Plane
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MHB Rotations, Reflections and Translations
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MHB Define matrix to get a row operation of type 1
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MHB The permutation induces on the set
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Graduate Question about the irreducible representation of a rank 2 tensor under SO(3)
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MHB How to Solve a Linear Equation System Using Row Reduction?
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Undergrad Linear Isomorphisms: Understand & Apply
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Undergrad Proving Linear Transformation of V with sin(x),cos(x) & ex
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Graduate Decomposing SU(4) into SU(3) x U(1)
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MHB Is $\phi(U)$ a Subspace of $\mathbb{R}^m$?
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Undergrad Understanding the Derivation of Reciprocal Lattice Basis from Equations 5 and 6
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Graduate Representations of finite groups -- Equivalent representations
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Graduate Representations of finite groups: Irreducible and reducible
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Graduate Difference Between Subgroup & Closed Subgroup of a Group
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High School What Does Skew Symmetry Imply for One-Dimensional Systems?
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Undergrad Rational functions in one indeterminate - useful concept?
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Undergrad 2 and 3 dimensional invariant subspaces of R4
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MHB Decide if the sets are subspaces or affine subspaces
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MHB Proving $\{w_1, \ldots , w_m\}$ is a Basis of $\text{Lin}(v_1, \ldots , v_k)$
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MHB How Does the Determinant of a Matrix Relate to the Area of a Parallelogram?
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High School Need an Equation for converting Vertical to horizontal FOV
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Undergrad How Can I Improve My Method for Translating Points on Coordinate Axes?
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MHB Relationship between three planes
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MHB Norms for a Linear Transformation .... Browder, Lemma 8.4 ....
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Undergrad Math for Blending Numbers: Find "X
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MHB Understanding Browder's Remarks on Linear Transformations
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MHB Proving Linear Dependence and Span in n-dimensional Space
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MHB Are the vectors linearly independent?
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Undergrad Condition for a pair of straight lines
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Graduate Is There a Closed Form for Airy Disk Eigenfunctions?
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High School I am 47 years old and I trying to learn Mathematics
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MHB Subset that satisfies all but one axioms of subspaces
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MHB What is the intersection of two spans?
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Graduate Solvability Of The Couniversal Mapping Problem On Products
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Issue with perspective projection?
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MHB Can These Mathematical Sets Be Considered Subspaces?
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Understanding Induced Maps: Types and Applications
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Undergrad Meaning of mapping R[X]->Maps[R,R]
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MHB Concatenating Lists: Associative but Not Commutative/Idempotent
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MHB Prove the statements : Vectors/Matrices
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High School Matrix Exponential: Researching Origins & Applications
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MHB What are the properties of distance?
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Undergrad Find the minimum and maximum value of a quadratic form
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Undergrad Find matrix of linear transformation and show it's diagonalizable
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MHB Short topical webpage title: Proving Properties of Unital Rings
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Undergrad Generalisation of Polarization identity
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Graduate Solutions of Matrix Equation A X B^T = C
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Undergrad Show isometry and find geometric meaning
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Undergrad The essence of the eigen problem
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Undergrad Is the Projection Matrix A^2=A Valid in R^4?
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Undergrad Proof of ##F## is an orthogonal projection if and only if symmetric
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MHB 4 problems regarding automorphisms/homomorphisms
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Undergrad Intersection of a plane with a segment in n dimensions
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Undergrad Prove that F^infinity is infinite dimensional
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Undergrad Why Does a Rank One Matrix with a=1 Still Have Solutions?
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