Multilinear algebraMultilinear algebra is a branch of mathematics that expands upon the principles of linear algebra. It extends the foundational theory of vector spaces by introducing the concepts of p-vectors and multivectors using Grassmann algebras. In a vector space of dimension n, the focus is primarily on using vectors. However, Hermann Grassmann and others emphasized the importance of considering the structures of pairs, triplets, and general multi-vectors, which offer a more comprehensive perspective.
Chebyshev distanceIn mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is named after Pafnuty Chebyshev. It is also known as chessboard distance, since in the game of chess the minimum number of moves needed by a king to go from one square on a chessboard to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to the edges of the board.
Outer productIn linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two coordinate vectors have dimensions n and m, then their outer product is an n × m matrix. More generally, given two tensors (multidimensional arrays of numbers), their outer product is a tensor. The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra.
HistorianA historian is a person who studies and writes about the past and is regarded as an authority on it. Historians are concerned with the continuous, methodical narrative and research of past events as relating to the human race; as well as the study of all history in time. Some historians are recognized by publications or training and experience. "Historian" became a professional occupation in the late nineteenth century as research universities were emerging in Germany and elsewhere.
Cross-cultural studiesCross-cultural studies, sometimes called holocultural studies or comparative studies, is a specialization in anthropology and sister sciences such as sociology, psychology, economics, political science that uses field data from many societies through comparative research to examine the scope of human behavior and test hypotheses about human behavior and culture. Cross-cultural studies is the third form of cross-cultural comparisons.
Hausdorff distanceIn mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff and Dimitrie Pompeiu. Informally, two sets are close in the Hausdorff distance if every point of either set is close to some point of the other set.
Mountaintop removal miningMountaintop removal mining (MTR), also known as mountaintop mining (MTM), is a form of surface mining at the summit or summit ridge of a mountain. Coal seams are extracted from a mountain by removing the land, or overburden, above the seams. This process is considered to be safer compared to underground mining because the coal seams are accessed from above instead of underground. In the United States, this method of coal mining is conducted in the Appalachian Mountains in the eastern United States.
