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Let us know more about Geometry of Sum of Squares
Sum of squares in geometry is not a very wide portion. Hence, it can be easy to understand and build assignment on.
Definition
Sum of squares in geometry is the mathematic approach to state the dispersion of the data points. Moreover, in analysis of regression, its aim is to obtain the data series that fits into the operation that may help to define the data series.
Usage
The sum of squares helps as a mathematical way to seek the operation that fits best with data. Hence, to determine sum of the squares,distance between individual line of the best fit and the data point is squared. Furthermore, all squares are summed up. Line of the best fit will minimise the value.Hence, to understand the usage, it is important that one must be able to know the fundamentals of it. This will facilitate to understand the topics below-
Polynomial SOS
Every form that is the SOS is a positive polynomial and though that preserve is not true always. Hilbert established that for the n=2, n=3 or m=1 and 2m= 4 the form is the SOS if possible. The similar is stands for analogue issue of the positive symmetric kinds.
Hence,
Generalizations
The basic generalisations are-
- Matrix SOS
- Matrix SMR
- Non-commutative polynomial SOS
Additionally, in non-commutativesituation, the non-commutative polynomial is the SOS only if it is the matrix positive.
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