In linear algebra, the rank of a matrix A is a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are many possible definitions of rank, including the size of the largest collection of linearly independent columns of A. Others are listed in the following section. The rank is one of the fundamental pieces of data associated with a matrix.

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Receptor Activator of Nuclear Factor κ B, also known as TRANCE Receptor, is a type I membrane protein that is expressed on the surface of osteoclasts and is involved in their activation upon ligand binding. RANK is also expressed on dendritic cells and facilitates immune signaling.

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  1. A row of people or things organized in a grid pattern, often soldiers [the corresponding term for the perpendicular columns in such a pattern is "file"].
    The front rank kneeled to reload while the second rank fired over their heads.
  1. one of the eight horizontal lines of squares on a chessboard [the corresponding term for a vertical line is "file"].
  1. In a pipe organ, a set of pipes of a certain quality for which each pipe corresponds to one key or pedal.
  2. One's position in a list sorted by a shared property such as physical location, population, or quality
    Based on your test scores, you have a rank of 23.
    The fancy hotel was of the first rank.
  3. The level of one's position in a class-based society
  4. a level in an organization such as the military
    Private First Class (PFC) is the lowest rank in the Marines.
    He rose up through the ranks of the company from mailroom clerk to CEO.
  5. a level in a scientific taxonomy system
    Phylum is the taxonomic rank below kingdom and above class.
  6. Maximal number of linearly independent columns (or rows) of a matrix.
  7. The dimensionality of an array or tensor .


  1. To place abreast, or in a line.
  2. To have a ranking.
    Their defense ranked third in the league.
  3. To assign a suitable place in a class or order; to classify.
  4. To take rank of; to outrank.


  1. Strong of its kind or in character; unmitigated; virulent; thorough; utter.
    rank treason; rank nonsense
  2. Strong in growth; growing with vigour or rapidity, hence, coarse or gross.
    rank grass; rank weeds
  3. Suffering from overgrowth or hypertrophy; plethoric.
  4. Causing strong growth; producing luxuriantly; rich and fertile.
    rank land
  5. Strong to the senses; offensive; noisome.
  6. Having a very strong and bad taste or odor.
    Your gym clothes are rank, bro – when d’you last wash ’em?
  7. Complete, used as an intensifier (usually negative, referring to incompetence).
    I am a rank amateur as a wordsmith.
  8. Gross, disgusting.
  9. Strong; powerful; capable of acting or being used with great effect; energetic; vigorous; headstrong.
  10. Inflamed with venereal appetite.


  1. Quickly, eagerly, impetuously.

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