Ad
related to: adding matrices
Search results
Results From The WOW.Com Content Network
In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. For a vector , v → {\displaystyle {\vec {v}}\!} , adding two matrices would have the geometric effect of applying each matrix transformation separately onto v → {\displaystyle {\vec {v}}\!} , then adding the transformed vectors.
Familiar properties of numbers extend to these operations on matrices: for example, addition is commutative, that is, the matrix sum does not depend on the order of the summands: A + B = B + A. [9] The transpose is compatible with addition and scalar multiplication, as expressed by (cA) T = c(A T) and (A + B) T = A T + B T. Finally, (A T) T = A.
Matrix addition is defined for two matrices of the same dimensions. The sum of two m × n (pronounced "m by n") matrices A and B, denoted by A + B, is again an m × n matrix computed by adding corresponding elements: [75] [76]
Extensions of this result can be made for more than two random variables, using the covariance matrix. Note that the condition that X and Y are known to be jointly normally distributed is necessary for the conclusion that their sum is normally distributed to apply.
Even in the case of matrices over fields, the product is not commutative in general, although it is associative and is distributive over matrix addition. The identity matrices (which are the square matrices whose entries are zero outside of the main diagonal and 1 on the main diagonal) are identity elements of the matrix product.
After months of speculating that right-hand man James Bender or even ex-husband Ant Anstead would join, The Flip Off premiere revealed that Haack has a team rallying behind her. Here's what we know.
Interior designer Grace Kaage's 2-year-old son, Christian, drew all over her white couch. See how she responded to her toddler drawing on her white furniture.
For n = 1, this matrix ring is isomorphic to R itself. For n > 1 (and R not the zero ring), this matrix ring is noncommutative. If G is an abelian group, then the endomorphisms of G form a ring, the endomorphism ring End(G) of G. The operations in this ring are addition and composition of endomorphisms.