Let $\text{trace}(AM)\ge0$ where $M$ is positive semidefinite, so we know that $\text{trace}(M)\ge0$ since the trace of a matrix is the sum of its eigenvalues.
Is $\text{trace}(A)\ge0$?
2026-03-25 18:55:39.1774464939
Let $\text{trace}(AM)\ge0$ where $M$ is psd, is $\text{trace}(A)\ge0$?
57 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related 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 EIGENVALUES-EIGENVECTORS
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- Show that this matrix is positive definite
- Is $A$ satisfying ${A^2} = - I$ similar to $\left[ {\begin{smallmatrix} 0&I \\ { - I}&0 \end{smallmatrix}} \right]$?
- Determining a $4\times4$ matrix knowing $3$ of its $4$ eigenvectors and eigenvalues
- Question on designing a state observer for discrete time system
- Evaluating a cubic at a matrix only knowing only the eigenvalues
- Eigenvalues of $A=vv^T$
- A minimal eigenvalue inequality for Positive Definite Matrix
- Construct real matrix for given complex eigenvalues and given complex eigenvectors where algebraic multiplicity < geometric multiplicity
Related Questions in TRACE
- How to show that extension of linear connection commutes with contraction.
- Basis-free proof of the fact that traceless linear maps are sums of commutators
- $\mathrm{tr}(AB)=\mathrm{tr}(BA)$ proof
- Similar 2x2 matrices of trace zero
- Basis of Image and kernel of Linear Transformation $\mathbb(M_{2,2})\rightarrow\mathbb(R^3) = (trace(A), 5*Trace(A), - Trace(A))$
- Replace $X$ with $\mbox{diag}(x)$ in trace matrix derivative identity
- Proving that a composition of bounded operator and trace class operator is trace class
- If $A \in \mathcal M_n(\mathbb C)$ is of finite order then $\vert \operatorname{tr}(A) \vert \le n$
- Characterisations of traces on $F(H)$
- "Symmetry of trace" passage in the proof of Chern Weil.
Related Questions in POSITIVE-SEMIDEFINITE
- Minimization of a convex quadratic form
- set of positive definite matrices are the interior of set of positive semidefinite matrices
- How to solve for $L$ in $X = LL^T$?
- How the principal submatrix of a PSD matrix could be positive definite?
- Hadamard product of a positive semidefinite matrix with a negative definite matrix
- The square root of a positive semidefinite matrix
- Optimization of the sum of a convex and a non-convex function?
- Proving that a particular set is full dimensional.
- Finding bounds for a subset of the positive semidefinite cone
- Showing a matrix is positive (semi) definite
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?
It's sufficient to consider diagonal matrices to see that $\text{trace}(A)$ can be anything.
Take for example $M=\text{diag}(1000,1,1)$ and $A=\text{diag}(1,-2,-3)$.