In linear algebra, a matrix unit is a matrix with only one nonzero entry with value 1.[1][2] The matrix unit with a 1 in the ith row and jth column is denoted as . For example, the 3 by 3 matrix unit with i = 1 and j = 2 is A vector unit is a standard unit vector.
A single-entry matrix generalizes the matrix unit for matrices with only one nonzero entry of any value, not necessarily of value 1.
Properties
[edit]The set of m by n matrix units is a basis of the space of m by n matrices.[2]
The product of two matrix units of the same square shape satisfies the relation where is the Kronecker delta.[2]
The group of scalar n-by-n matrices over a ring R is the centralizer of the subset of n-by-n matrix units in the set of n-by-n matrices over R.[2]
The matrix norm (induced by the same two vector norms) of a matrix unit is equal to 1.
When multiplied by another matrix, it isolates a specific row or column in arbitrary position. For example, for any 3-by-3 matrix A:[3]
References
[edit]- ^ Artin, Michael. Algebra. Prentice Hall. p. 9.
- ^ a b c d Lam, Tsit-Yuen (1999). "Chapter 17: Matrix Rings". Lectures on Modules and Rings. Graduate Texts in Mathematics. Vol. 189. Springer Science+Business Media. pp. 461–479.
- ^ Marcel Blattner (2009). "B-Rank: A top N Recommendation Algorithm". arXiv:0908.2741 [physics.data-an].
Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
View the detailed Guide of Psilotum nudum: Detailed Study Of Psilotum Nudum (Whisk Fern), Classification, Anatomy, Reproduction