Question

Let $W_1$ and $W_2$ be subspaces of a finite dimensional inner product space space. Prove that $(W_1 \cap W_2)^\perp=W_1^\perp + W_2^\perp $

score 5.9k · Answer 1 · 2014-08-16 02:20:40

Let $W_1$ and $W_2$ be subspaces of a finite dimensional inner product space space. Prove that $(W_1 \cap W_2)^\perp=W_1^\perp + W_2^\perp $

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List Question

Let $W_1$ and $W_2$ be subspaces of a finite dimensional inner product space space. Prove that $(W_1 \cap W_2)^\perp=W_1^\perp + W_2^\perp $

What is the difference between isometric and unitary operators on a Hilbert space?

Does $S^\bot+T^\bot = (S\cap T)^\bot$ hold in infinite-dimensional spaces?

Let $A$ be an invertible , prove that there exist positive constants $c_1$ and $c_2$ such that $c_1X^tX\leq X^tA^tAX\leq c_2X^tX $

Showing the conjugate symmetric property of an inner product when we don't know if our field is $\mathbb{C}$.

Intersection of nested closed bounded convex sets in Euclidean space

An inner product inequality

What's the connection between "hyperbolic" inner product spaces and the hyperbolic plane?

When is $V=U\oplus U^{\perp}$?

What does "$S\times S\rightarrow R$

Is an inner product continuous?

Is every basis of a finite-dimensional vector space orthonormal with respect to some inner product?

Need verification - Given a Hermitian matrix and two eigenvectors corresponding to distinct eigenvalues, show x and y are orthogonal.

Prove that function is inner product

What is the closest self-adjoint (positive) operator to a given operator?

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