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 Why Are Nilpotent Elements Significant in Ring Theory?
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MHB Applying rotation matrix to make inclined plane flat again
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Undergrad Free Groups - Dmmit & Fooote - Section 6.3
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MHB List the elements of the field F = F3[x] / < x2 + 1 >
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MHB Tensor Products - Issue with Cooperstein, Theorem 10.3
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MHB Free Groups - Dummit & Fooote - Section 6.3
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Graduate How to Solve the Inequality x^2 + 2ix + 3 < 0?
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MHB What are some important properties of the Commutator Group of D_n?
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MHB Linear Programming word problems
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MHB Why Can't a Proper Normal Subgroup Contain a Sylow Normalizer in a Group?
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Undergrad A real matrix and its inverse share the same eigenvectors?
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Undergrad Sylow subgroup of some factor group
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Undergrad Proof of Existence of Tensor Product .... Cooperstein ....
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MHB Number of Orbits: Showing Equality of Group G and G_a
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Undergrad Properties of Tensor Products - Cooperstein, Theorem 10.3
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MHB G contains a normal p-Sylow subgroup
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Undergrad Tensor Products - Issue with Cooperstein, Theorem 10.3
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MHB Show that it is a normal subgroup of S4
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MHB How can we find all the normal subgroups?
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MHB Proof: Every Subgroup of Cyclic $H$ is Normal in $G$
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MHB Show that the group is not simple
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Undergrad True or False: A Linear System Must Have a Unique Solution
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High School Trying to understand function transformations
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Graduate Eigenstates of "summed" matrix
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MHB Multiplicative group of matrices is nilpotent
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Undergrad Can you Explain this SVD Application?
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Undergrad Question about using matrices for differential equations
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MHB What Are the Composition Series for \(A_4\) and \(S_3 \times \mathbb{Z}_2\)?
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Undergrad Transformation of Tensor Components
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MHB Is \(\pi\) Algebraic of Degree 3 Over Any Extension of \(\mathbb{Q}\)?
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Undergrad Basis of a Tensor Product - Cooperstein - Theorem 10.2
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MHB Normal series and composition series
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Graduate Isomorphism between a linear space and its dual
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MHB Is Every Group of Order 135 Nilpotent?
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Fermat's Theorem: Proven by Euler and By Me?
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MHB The group is isomorphic to one of the groups
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MHB Show that each such group is solvable
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MHB Inequality related to number of p-Sylow subgroups
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Graduate Artinian rings are noetherian, why does this make sense?
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MHB Proving $\text{GL}_{2}(R): Showing Homomorphism & Isomorphism
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Undergrad Conditions on negative definiteness
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MHB Show that the intersection is a pp -Sylow subgroup
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Graduate Are Minimal Left Ideals in Hassani's Algebra Always Trivial?
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MHB How Do You Find the Multiplicative Inverse in \( Z_{360}[x] \)?
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MHB Is \( f(P) \) a \( p \)-Sylow Subgroup of \( H \)?
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MHB Prove: Q(ζp)=Q(ζip) | Cyclotomic Polynomials
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MHB Math Problem: Rotation on z Axis
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MHB Principle Ideal in F[x] & Primitive nth root of unity
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Undergrad Basis of a Tensor Product - Theorem 10.2 - Another Question
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Undergrad Proof that the general solution of a linear equation is....
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MHB Proof of Existence of Tensor Product: Cooperstein Theorem 10.1
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Undergrad Proof of Existence of Tensor Product .... Further Question ...
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MHB Understanding the Chinese Remainder Theorem for $\mathbb{Z}^{\times} _{20}$
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MHB How many necklaces can we create?
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MHB Linear Algebra: Analyzing A Linear Transformation
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MHB Theorem 6.10 in Knapp's Basic Algebra: Exploring Bilinearity & Descending Maps
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Undergrad Understanding [T]_gamma and Its Purpose in Linear Transformations
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Undergrad Tensor Product - Knapp - Theorem 6.10 .... Further Question
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Undergrad Tensor Product - Knapp, Chapter VI, Section 6
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MHB Tensor Product - Knapp, Chapter VI, Section 6
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MHB Proving Equivalence of $g' \in Hg$, $g'g^{-1} \in H$, and $Hg = Hg'$
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MHB Zero Divisor Help: Prove & Example
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MHB Understanding Rings: Example of Homomorphism/Isomorphism
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MHB Solving the Mystery of the Table: Explaining $g = (123)$
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MHB Can a group of order $2^6\cdot 5^6$ be simple?
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MHB Find Left Cosets of Subgroup in $\mathbb{Z}_{15}, D_4$
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MHB Proving Two Rings Are Isomorphic
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MHB Boost Your Cosine-Sine Isotherm Sketching Skills | Expert Tips & Guidance
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MHB How to Determine the Order of \( g^8 \) in a Group?
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Undergrad Confused on definition of projection
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Undergrad Difference between 'Field' (algebra) and 'Field' (geometry)
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Undergrad Aren't all linear operators one-to-one and onto?
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MHB Does Lemma 3 in Winitzki's Tensor Product Dimension Section Clarify Covectors?
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MHB The Uniqueness of a Tensor Product
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MHB The probability that two elements commute
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MHB How can we prove the equality of orders for finite subgroups of a group?
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MHB Decide h so that the linear system has infinite solutions
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Undergrad Why only normal subgroup is used to obtain group quotient
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MHB Finding the Equation of a Plane Perpendicular to a Given Line
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Undergrad Calculating the number of real parameters of a unitary matri
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MHB Solve System of Equations: Unique Solution & Geometric Explanation
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Undergrad How Does Covector Existence Relate to Tensor Dimensions in Winitzki's Lemma 3?
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Undergrad Coefficients of a vector regarded as a function of a vector
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MHB Cartesian Equation of the Plane Passing Through Two Vectors
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MHB Linear transformation and its matrix
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MHB Proving $(T^2-I)(T-3I) = 0$ for Linear Operator $T$
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High School Is the Null Space of an Operator Defined by Its Zero Eigenvalue?
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MHB Is There a Solution for 6 Degree of Freedom Solid Body Movement Equations?
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MHB Linear Subspaces: Properties and Examples
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MHB Field Extensions for polynomials
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MHB Dual Vector Space and Dual Basis - another question - Winitzki Section 1-6
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MHB How Are Coefficients of a Vector Linear Functions of the Vector?
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MHB Finding equation normal to a plane and certain point
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MHB How do you change the basis of vectors in $\mathbb{R}^3$?
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MHB How Does E Relate to Q[x]/(x²+x+1) in Complex Algebra?
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MHB Help with $(iii)$ of Math Problem on MHB
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High School What Does Dimension Mean in Vector Spaces?
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MHB Showing That $(AB)x = A(Bx)$: A Clue!
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MHB Which is the velocity and the angle?
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MHB Dimension of $m \times n$ Matrices: Finding Basis
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