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Definition

The PIVOT VECTOR SPACE APPROACH is a novel technique of audio-video mixing which automatically selects the best audio clip from the available database, to be mixed with the given video shot. Till the development of this technique, audio-video mixing is a process that could be done only by professional audio-mixing artists. However employing these artists is very expensive and is not feasible for home video mixing. Besides, the process is time-consuming and tedious.

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We are familiar with the properties of finite dimensional vector spaces over a field. Many of the results that are valid in finite dimensional vector spaces can very well be extended to infinite dimensional cases sometimes with slight modifications in definitions. But there are certain results that do not hold in infinite dimensional cases. Here we consolidate some of those results and present it in a readable form.
We present the whole work in three chapters. All those concepts in vector spaces and linear algebra which we require in the seque ....etc

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The PIVOT VECTOR SPACE APPROACH is a novel technique of audio-video mixing which automatically selects the best audio clip from the available database, to be mixed with the given video shot. Till the development of this technique, audio-video mixing is a process that could be done only by professional audio-mixing artists. However employing these artists is very expensive and is not feasible for home video mixing. Besides, the process is time-consuming and tedious. In todayâ„¢s era, significant advances are happening constantly in the field ....etc

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Infinite Dimensional Vector Space

Introduction
We are familiar with the properties of finite dimensional vector spaces over a field. Many of the results that are valid in finite dimensional vector spaces can very well be extended to infinite dimensional cases sometimes with slight modifications in definitions. But there are certain results that do not hold in infinite dimensional cases. Here we consolidate some of those results and present it in a readable form.

We present the whole work in three chapters. All those concepts in vector sp ....etc

[:=Read Full Message Here=:]

Definition

The PIVOT VECTOR SPACE APPROACH is a novel technique of audio-video mixing which automatically selects the best audio clip from the available database, to be mixed with the given video shot. Till the development of this technique, audio-video mixing is a process that could be done only by professional audio-mixing artists. However employing these artists is very expensive and is not feasible for home video mixing. Besides, the process is time-consuming and tedious.

In today's era, significant advances are happening constantly i ....etc

[:=Read Full Message Here=:]

We are familiar with the properties of finite dimensional vector spaces over a field. Many of the results that are valid in finite dimensional vector spaces can very well be extended to infinite dimensional cases sometimes with slight modifications in definitions. But there are certain results that do not hold in infinite dimensional cases. Here we consolidate some of those results and present it in a readable form.

We present the whole work in three chapters. All those concepts in vector spaces and linear algebra which we require in the seq ....etc

[:=Read Full Message Here=:]

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