## RANK

### Rank

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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### RANK

**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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### rank

#### Noun

- 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.

- one of the eight horizontal lines of squares on a chessboard [the corresponding term for a vertical line is "file"].

- In a pipe organ, a set of pipes of a certain quality for which each pipe corresponds to one key or pedal.
- 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.**

- The level of one's position in a class-based society
- 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.

- a level in a scientific taxonomy system
*Phylum is the taxonomic***rank**below kingdom and above class.

- Maximal number of linearly independent columns (or rows) of a matrix.
- The dimensionality of an array or tensor .

#### Verb

- To place abreast, or in a line.
- To have a ranking.
*Their defense***ranked**third in the league.

- To assign a suitable place in a class or order; to classify.
- To take rank of; to outrank.

#### Adjective

- Strong of its kind or in character; unmitigated; virulent; thorough; utter.
*rank**treason;***rank**nonsense

- Strong in growth; growing with vigour or rapidity, hence, coarse or gross.
*rank**grass;***rank**weeds

- Suffering from overgrowth or hypertrophy; plethoric.
- Causing strong growth; producing luxuriantly; rich and fertile.
*rank**land*

- Strong to the senses; offensive; noisome.
- Having a very strong and bad taste or odor.
*Your gym clothes are***rank**, bro – when d’you last wash ’em?

- Complete, used as an intensifier (usually negative, referring to incompetence).
*I am a***rank**amateur as a wordsmith.

- Gross, disgusting.
- Strong; powerful; capable of acting or being used with great effect; energetic; vigorous; headstrong.
- Inflamed with venereal appetite.

#### Adverb

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