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Hermann Hankel (14 February 1839 – 29 August 1873) was a German mathematician. Having worked on mathematical analysis during his career, he is best known for introducing the Hankel transform and the Hankel matrix .
Hankel matrices are formed when, given a sequence of output data, a realization of an underlying state-space or hidden Markov model is desired. [3] The singular value decomposition of the Hankel matrix provides a means of computing the A , B , and C matrices which define the state-space realization. [ 4 ]
In control theory, Hankel singular values, named after Hermann Hankel, provide a measure of energy for each state in a system. They are the basis for balanced model reduction, in which high energy states are retained while low energy states are discarded. The reduced model retains the important features of the original model.
In psychology, the four stages of competence, or the "conscious competence" learning model, relates to the psychological states involved in the process of progressing from incompetence to competence in a skill. People may have several skills, some unrelated to each other, and each skill will typically be at one of the stages at a given time.
The psychology of learning refers to theories and research on how individuals learn. There are many theories of learning. Some take on a more behaviorist approach which focuses on inputs and reinforcements. [1] [2] [3] Other approaches, such as neuroscience and social cognition, focus more on how the brain's organization and structure influence ...
One of the first mathematicians to appreciate Grassmann's ideas during his lifetime was Hermann Hankel, whose 1867 Theorie der complexen Zahlensysteme. [5] […], he developed […] some of Hermann Grassmann's algebras and W.R. Hamilton's quaternions. Hankel was the first to recognise the significance of Grassmann's long-neglected writings and ...
The spacing effect demonstrates that learning is more effective when study sessions are spaced out. This effect shows that more information is encoded into long-term memory by spaced study sessions, also known as spaced repetition or spaced presentation, than by massed presentation ("cramming").
Gilbert Harman (May 26, 1938 [3] – November 13, 2021 [4]) was an American philosopher, who taught at Princeton University from 1963 [5] until his retirement in 2017. [6] He published widely in philosophy of language, cognitive science, philosophy of mind, ethics, moral psychology, epistemology, statistical learning theory, and metaphysics.