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In this manner log function is a multi-valued function (often referred to as a "multifunction" in the context of complex analysis). A branch cut, usually along the negative real axis, can limit the imaginary part so it lies between −π and π. These are the chosen principal values. This is the principal branch of the log function.
Selection principle. In mathematics, a selection principle is a rule asserting the possibility of obtaining mathematically significant objects by selecting elements from given sequences of sets. The theory of selection principles studies these principles and their relations to other mathematical properties.
Dimensionality reduction. Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can ...
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instead. In developing the analogue for the complex logarithm, there is an additional complication: the definition of the complex integral requires a choice of path. . Fortunately, if the integrand is holomorphic, then the value of the integral is unchanged by deforming the path (while holding the endpoints fixed), and in a simply connected region (a region with "no holes"), any path from to ...
The principal–agent problem refers to the conflict in interests and priorities that arises when one person or entity (the "agent") takes actions on behalf of another person or entity (the "principal"). [1] The problem worsens when there is a greater discrepancy of interests and information between the principal and agent, as well as when the ...
Principal component analysis ( PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing . The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.