Say $\text{Spec}(\mathbf{X})$ is a set of eigenvalues of a real positive definite matrix $\mathbf{X}$.
How do I express $$ \sum_{\lambda\in\text{Spec}(\mathbf{X})} \lambda \log \lambda$$ without explicitly finding the eigenvalues?
2026-05-06 04:34:57.1778042097
Expressing $ \sum_{\lambda\in\text{Spec}(\mathbf{X})} \lambda \log \lambda$
44 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 LOGARITHMS
- Confirmation of Proof: $\forall n \in \mathbb{N}, \ \pi (n) \geqslant \frac{\log n}{2\log 2}$
- Extracting the S from formula
- How to prove the following inequality (log)
- Rewriting $(\log_{11}5)/(\log_{11} 15)$
- How to solve this equation with $x$ to a logarithmic power?
- Show that $\frac{1}{k}-\ln\left(\frac{k+1}{k}\right)$ is bounded by $\frac{1}{k^2}$
- Why do we add 1 to logarithms to get number of digits?
- Is my method correct for to prove $a^{\log_b c} = c^{\log_b a}$?
- How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?
- Unusual Logarithm Problem
Related Questions in POWER-SERIES
- Conditions for the convergence of :$\cos\left( \sum_{n\geq0}{a_n}x^n\right)$
- Power series solution of $y''+e^xy' - y=0$
- Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$
- Pointwise and uniform convergence of function series $f_n = x^n$
- Divergence of power series at the edge
- Maclaurin polynomial estimating $\sin 15°$
- Computing:$\sum_{n=0}^\infty\frac{3^n}{n!(n+3)}$
- How to I find the Taylor series of $\ln {\frac{|1-x|}{1+x^2}}$?
- Convergence radius of power series can be derived from root and ratio test.
- Recognizing recursion relation of series that is solutions of $y'' + y' + x^2 y = 0$ around $x_0 = 0$.
Related Questions in NUMERICAL-LINEAR-ALGEBRA
- sources about SVD complexity
- Showing that the Jacobi method doesn't converge with $A=\begin{bmatrix}2 & \pm2\sqrt2 & 0 \\ \pm2\sqrt2&8&\pm2\sqrt2 \\ 0&\pm2\sqrt2&2 \end{bmatrix}$
- Finding $Ax=b$ iteratively using residuum vectors
- Pack two fractional values into a single integer while preserving a total order
- Use Gershgorin's theorem to show that a matrix is nonsingular
- Rate of convergence of Newton's method near a double root.
- Linear Algebra - Linear Combinations Question
- Proof of an error estimation/inequality for a linear $Ax=b$.
- How to find a set of $2k-1$ vectors such that each element of set is an element of $\mathcal{R}$ and any $k$ elements of set are linearly independent?
- Understanding iterative methods for solving $Ax=b$ and why they are iterative
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?