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Prove that Hilbert Space is a Metric Space?

The question doesn't make sense, or alternatively it is true by definition. A Hilbert Space is a complete inner product space - complete in the metric induced by the norm defined by the inner product over the space. In other words an inner product space is a vector space with an inner product defined on it. An inner product then defines a norm on the space, and every norm on a space induces a metric. A Hilbert Space is thus also a complete metric space, simply where the metric is induced by the inner product.


If T is a linear operator on an inner product space is the norm of Tx equals norm of x if and only if inner product of Tx and Ty equals inner product of x and y?

no -- consider linear map sending entire source space to zero of target space


What is the significance of the Hilbert-Schmidt inner product in the context of functional analysis?

The Hilbert-Schmidt inner product is important in functional analysis because it allows for the definition of a norm on the space of square-integrable functions. This inner product helps in studying the convergence of sequences of functions and in defining orthogonal projections in Hilbert spaces.


Is it possible for the inner product to be negative?

Yes, it is possible for the inner product to be negative.


When was Inner Space - album - created?

Inner Space - album - was created in 1973.


What is the duration of Destination Inner Space?

The duration of Destination Inner Space is 1.38 hours.


When was Destination Inner Space created?

Destination Inner Space was created in 1966-05.


What is the ISBN of The Inner Reaches of Outer Space?

The ISBN of The Inner Reaches of Outer Space is 1577312090.


When was The Inner Reaches of Outer Space created?

The Inner Reaches of Outer Space was created in 1986.


How many pages does The Inner Reaches of Outer Space have?

The Inner Reaches of Outer Space has 160 pages.


What is the best hair care product to use when you have split ends?

Use products from Suave and Garnier to strengthen your hair and release its inner beauty


Where can you download Operation Inner Space.?

Software Dynamics, the makers of Operation: Inner Space, have a free demo on their website.