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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 Is this a valid proof for the invertibility of $\Phi$?
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Undergrad Proof that every basis has the same cardinality
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Undergrad Nonempty Subspace: Proving 0u = 0
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MHB Show That $F(S)$ Is the Smallest Subfield of $K$
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MHB Show that Q[π] is not a subset of Q(π)
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Undergrad Questions about linear transformations
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Undergrad Understanding rectangular matrices
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MHB Finding the Matrix Associated with a Linear Mapping on a Real Matrix
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Graduate Question on Cauchy-Schwarz inequality
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MHB Find Group $G$ with Infinite Order Element: Ablien Not Allowed
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MHB Proving Divisibility of Polynomials in Field Extensions
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Undergrad Finitely Generated Modules .... another question
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Undergrad Finitely Generated Modules and Their Submodules ....
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Undergrad Vector Functions: v(r) Explained
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MHB Determinant of matrix with Aij = min(i, j)
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MHB Finitely Generated Modules and Their Submodules .... Berrick and Keating ....
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Undergrad Components of functions in vector spaces
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Graduate For finite dimension vector spaces, all norms are equivalent
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High School Matrices concept confusion....
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MHB I=<f> is maximal iff f is irreducible
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MHB Proving Convex Set Properties to Showing the Convexity of X-Y
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Undergrad I don't quite understand what i read
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MHB Please, help with system of equations
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MHB How can the convexity of a disk be proved using linear algebra?
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Undergrad Finitely Generated Ideals and Noetherian Rings
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MHB Finite Extension Simple iff Purely Inseparable Closure Simple
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MHB Show That F[u]=F(u): Proving with Theorem
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MHB Finitely Generated Ideals and Noetherian Rings
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Undergrad Triangular Matrix RIngs .... Lam, Proposition 1.17
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Undergrad How Do You Prove a Matrix Ring is Right Artinian But Not Left Artinian?
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Undergrad Quick question about Lagrange's theorem
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Undergrad Linear least-squares method and row multiplication of matrix
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MHB Proving disjoint of Kernel and Image of a linear mapping
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MHB How Do You Prove a Mapping is Surjective?
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MHB Triangular Matrix RIngs .... Lam, Proposition 1.17
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Undergrad Triangular Matrix RIngs .... Another Question
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MHB Triangular Matrix Rings .... Another Question
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MHB Is G an Abelian Group Given Specific Conditions?
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Undergrad Why do eigenvectors stay the same when a matrix is squared?
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Undergrad Concrete Examples of Exact Sequences in Linear Algebra
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MHB What are the ideals of the matrix ring?
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MHB Maximal Ideals - Exercise 5.1 (ii) Rotman AMA
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MHB Example on Triangular Rings - Lam, Example 1.14
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Undergrad Example on Triangular Rings - Lam, Example 1.14
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Undergrad Points of a finite projective line
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MHB Approaching Question C1: Finding Roots of Elements in a Field
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High School How do we know if something is vector or scalar quantity?
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Undergrad Expanding linear independent vectors
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Undergrad Understanding Subspaces: Definition and Examples | PF Study Guide
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Undergrad How to Construct an Orthonormal Basis for a 2D Subspace in Linear Algebra?
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Graduate Expectation operation for covariance calculation
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Undergrad Coordinate transformation of a vector of magnitude zero
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Undergrad Fundamental Theorem of Arithmetic - Bhattacharya et al
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MHB Fundamental Theorem of Arithmetic - Bhattacharya et al - Ch. 2, Section 1
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MHB Maximal Ideals - Exercise 5.1 (iii) Rotman AMA
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Undergrad Are the columns space and row space same for idempotent matrix?
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MHB A little problem on exact sequences, part 2.
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MHB Prime and Maximal Ideals in PIDs .... Rotman, AMA Theorem 5.12
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Undergrad Newton's formula for the sums of powers of roots?
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MHB Prove Z7 is a Ring Under + and x Operations
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Undergrad Prime and Maximal Ideals in PIDs ... Rotman, AMA Theorem 5.12
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MHB How Does the Correspondence Theorem for Rings Prove Maximal Ideals?
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Undergrad Maximal Ideals and the Correspondence Theorem for Rings
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MHB Normal Extensions and Normal Subgroups
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MHB A little problem on exact sequences.
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Undergrad Constructing a vector from a point
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Undergrad Transpose Property (where's my mistake)
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Undergrad A double in this example problem
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Undergrad Show that the diagonals are perpendicular using vectors
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High School Vector perpendicular to a plane defined by two vectors
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MHB Vector in 3d with given by magnitude and angle
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Undergrad Use Lorentz Force to Find Magnetic Field Components
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Undergrad Can RREF be used for any size matrix?
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Undergrad Matrix Component Equation: Solving for B with Known Scalar and Indices
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Undergrad Kronecker Delta summation (easy)
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High School The equation relating a vector to a unit vector
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MHB Prove: \(F(a,b)^*=F(a) \cup F(b)\)
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MHB Ice cream & yogurt matrices problem
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Undergrad Two-sided Prinicipal Ideal - the Noncommutative Case - D&F
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MHB Why Is the Set {ras | r, s ∈ R} Not a Two-Sided Ideal in Noncommutative Rings?
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Undergrad Understanding SU(2) Representations and Their Role in Particle Physics
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Undergrad Module Over a Division Ring - Blyth Theorem 1.1, Part 4
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Undergrad State of a Generator in Representation Theory
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High School Tensor Calculus vs Tensor Analysis?
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Undergrad What is the name of the matrix decomposition with specific properties?
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Undergrad No problem, it's always good to have multiple sources!
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MHB Finding the zero vector of a sinusoidal set
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MHB Submodules A + B and A intersect B .... Blyth Ch. 2
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Undergrad Submodules A + B and A intersect B .... Blyth Ch. 2
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MHB Theorem 2.3: Submodule Generation by Family of Submodules - T. S. Blyth
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Undergrad Submodule Generated by Family of Submodules -Simple Question
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High School Is the Inverse of this Matrix Possible?
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Undergrad Interpretation of direct product of Hilbert spaces
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Undergrad Coordinate System: Understanding Polar Vectors
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Graduate What Is the Spectrum of a Linear Operator in L2 Spaces?
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MHB Making a Right R-module Into a Left R-Module - Bland, page 26 ....
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Undergrad Split Exact Sequences .... Bland, Proposition 3.2.7
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MHB Module Over a Division Ring - Blyth Theorem 1.1, Part 4
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MHB How Does Condition (2) Imply Condition (3) in Bland's Proposition 3.2.7?
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Undergrad Eigenvalue as a generalization of frequency
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