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A matrix is said to have full rank if its rank equals the largest possible for a matrix of the same dimensions, which is the lesser of the number of rows and columns. A matrix is said to be rank-deficient if it does not have full rank. The rank deficiency of a matrix is the difference between the lesser of the number of rows and columns, and ...
Traditionally, Assistant Professor has been the usual entry-level rank for faculty on the "tenure track", although this depends on the institution and the field.Then, promotion to the rank of Associate Professor and later Professor (informally, "Full Professor") indicates that significant work has been done in research, teaching and institutional service.
Academic rank (also scientific rank) is the rank of a scientist or teacher in a college, high school, university or research establishment. The academic ranks indicate relative importance and power of individuals in academia. The academic ranks are specific for each country, there is no worldwide-unified ranking system.
Higher tiers represent a more favorable ranking. The letters are inspired by grading in education , [ 1 ] especially in Japanese culture , which may include an 'S' grade. A tier list is a concept originating in video game culture where playable characters or other in-game elements are subjectively ranked by their respective viability as part of ...
A has full rank: rank A = n. A has a trivial kernel: ker(A) = {0}. The linear transformation mapping x to Ax is bijective; that is, the equation Ax = b has exactly one solution for each b in K n. (Here, "bijective" can equivalently be replaced with "injective" or "surjective") The columns of A form a basis of K n. (In this statement, "basis ...
A research professor is usually the most senior rank of a research-focused career pathway in those countries and is regarded as equal to the ordinary full professor rank. Most often they are permanent employees, and the position is often held by particularly distinguished scholars; thus the position is often seen as more prestigious than an ...
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When attending functions as "Colonel of the Regiment", the titleholder wears the regimental uniform with rank insignia of (full) colonel, regardless of their official rank. A member of the Royal Family is known as a Royal Colonel. A Colonel of the Regiment is expected to work closely with a regiment and its Regimental Association. [citation needed]