Let $A, B \in \Bbb C^{n \times n}$ such that $A$ is nilpotent but $B$ is non-nilpotent satisfying $AB+BA=O$. Then, $AX+XB=B$ has unique solution. True or false?
I don't understand how to approach this problem. Any hint, please?
2026-03-28 08:46:16.1774687576
Does $AX+XB=B$ have a unique solution?
116 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in MATRICES
- How to prove the following equality with matrix norm?
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Powers of a simple matrix and Catalan numbers
- Gradient of Cost Function To Find Matrix Factorization
- Particular commutator matrix is strictly lower triangular, or at least annihilates last base vector
- Inverse of a triangular-by-block $3 \times 3$ matrix
- Form square matrix out of a non square matrix to calculate determinant
- Extending a linear action to monomials of higher degree
- Eiegenspectrum on subtracting a diagonal matrix
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
Related Questions in MATRIX-EQUATIONS
- tensor differential equation
- Can it be proved that non-symmetric matrix $A$ will always have real eigen values?.
- Real eigenvalues of a non-symmetric matrix $A$ ?.
- How to differentiate sum of matrix multiplication?
- Do all 2-variable polynomials split into linear factors over the space of $2 \times 2$ complex matrices?
- Big picture discussion for iterative linear solvers?
- Matrix transformations, Eigenvectors and Eigenvalues
- Jordan chevaley decomposition and cyclic vectors
- If $A$ is a $5×4$ matrix and $B$ is a $4×5$ matrix
- Simplify $x^TA(AA^T+I)^{-1}A^Tx$
Related Questions in NILPOTENCE
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- A question about Maschke theorem
- A question on the group algebra
- The radical of the algebra $ A = T_n(F)$ is $N$, the set of all strictly upper triangular matrices.
- Is $A-B$ never normal?
- Nilradical of a noncommutative Ring
- Nil(Nil(R) = Nil(R) meaning
- Ideal Generated by Nilpotent Elements is a Nilpotent Ideal
- Inequality for nilpotent matrices: $\dim\ker A^2 > \dim\ker A$
- Nilpotent $4 × 4$ matrix
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?