Lewis(1995) " The convex analysis of unitarily invariant matrix functions " states the result by von neumann that $\langle X,Y \rangle \leq \langle \sigma_X,\sigma_Y \rangle$. Does anyone know any easy proof or reference for it. i couldnt understand the reference cited in the paper.
2026-03-25 22:09:53.1774476593
Bounds for Matrix Inner Product based on singular values
118 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
- 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)
- Dimension of solution space of homogeneous differential equation, proof
Related Questions in INNER-PRODUCTS
- Inner Product Same for all Inputs
- How does one define an inner product on the space $V=\mathbb{Q}_p^n$?
- Inner Product Uniqueness
- Is the natural norm on the exterior algebra submultiplicative?
- Norm_1 and dot product
- Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?
- Orthonormal set and linear independence
- Inner product space and orthogonal complement
- Which Matrix is an Inner Product
- Proof Verification: $\left\|v-\frac{v}{\|v\|}\right\|= \min\{\|v-u\|:u\in S\}$
Related Questions in MATRIX-DECOMPOSITION
- Real eigenvalues of a non-symmetric matrix $A$ ?.
- Swapping row $n$ with row $m$ by using permutation matrix
- Block diagonalizing a Hermitian matrix
- $A \in M_n$ is reducible if and only if there is a permutation $i_1, ... , i_n$ of $1,... , n$
- Simplify $x^TA(AA^T+I)^{-1}A^Tx$
- Diagonalize real symmetric matrix
- How to solve for $L$ in $X = LL^T$?
- Q of the QR decomposition is an upper Hessenberg matrix
- Question involving orthogonal matrix and congruent matrices $P^{t}AP=I$
- Singular values by QR decomposition
Related Questions in SINGULAR-VALUES
- Singular Values of a rectangular matrix
- Connection between singular values, condition and well-posedness
- Does the product of singular values of a rectangular matrix have a simple expression?
- Clarification on the SVD of a complex matrix
- Intuitive explanation of the singular values
- What are the characteristics that we can use to identify polynomials that have singular points?
- Zolotarev number and commuting matrices
- Spectral norm of block and square matrices
- Why is the Schmidt decomposition of an operator not unique?
- Smallest singular value of full column rank matrix
Related Questions in MATRIX-NORMS
- Inequality regarding norm of a positive definite matrix
- Operator norm calculation for simple matrix
- Equivalence of computing trace norm of matrix
- Spectral norm minimization
- Frobenius and operator norms of rank 1 matrices
- Prove the induced matrix norm $\|A\|_\infty = \max_i \| a^*_i \|_1$
- $l_2 \rightarrow l_\infty$ induced matrix norm
- Is it possible to upper bound this family of matrices in operator norm?
- Upper bound this family of matrices in induced $2$-norm
- Operator norm (induced $2$-norm) of a Kronecker tensor
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?
This is called the von-Neumann trace inequality. For a reference: this is given in Horn and Johnson's Matrix Analysis as Theorem 7.4.1.1. For a more powerful result, you could use corollary IV.2.6 of Bhatia's Matrix Analysis.