An m-by- n matrix is called a column matrix if n = 1 (i.e., if it consists of just one column), a row matrix if m = 1 (i.e., if it consists of just one row), and a square matrix if m = n. The transpose of an m-by- n matrix A is the n-by- m matrix A ┬ obtained by flipping A over diagonally, so that the kth row becomes the kth column and vice versa. The matrix A given above may be represented more briefly as A = ( a ij : 1 ≤ i ≤ m 1 ≤ j ≤ n), or still more briefly as ( a ij) if no confusion will result. We say a ij is the element (or component) in row i and column j. With m rows and n columns, where each a ij is an element of K. We currently think of using domain decomposition ideas in MRILU using message passing for communication between processors.Ī =
Matrix meaning code#
Our final conclusion is that for distributed memory computers the code must be changed more drastically in order to get reasonable speedup. Moreover we miss the vectorization possibilities of the CRAY which are well usable for our type of problems. Compared to results we had on the CRAY J90 we see that larger chunks are necessary to get reasonable speedup. This is caused by too fine grained parallelizable parts.
![matrix meaning matrix meaning](https://i.ytimg.com/vi/bOUXewOQ1GU/maxresdefault.jpg)
Hence, though not all parts were parallelized, it is already clear that for MRILU the data parallel programming approach will not give great speedup on distributed memory computers, a factor 2 to 3 at most. Due to Amdahl’s law this will also restrict the overall speedup. Secondly, the nearly independent set selection and the reordering procedure were only partially parallelizable and therefore gave only limited speedup. However for large matrices the memory accesses and the communication time between node boards will have a large (negative) impact on the ran time. Firstly, matrix-vector and matrix-matrix multiplication with CSR-matrices give reasonable speedup. The experiments on the TERAS reported in this paper lead us to the following conclusions. Richard Levine, Fred Wubs, in Parallel Computational Fluid Dynamics 2001, 2002 10 Conclusions , where k 1, k 2, … , k n is any set of nonzero scalars. (a)ĭetermine which of the following sets are bases for P 3. (a)ĭetermine which of the following sets are bases for P 2. (c)ĭetermine which of the following sets are bases for P 1. (a)ĭetermine which of the following sets are bases for M 2 × 2. (a)ĭetermine which of the following sets are bases for R 3, considered as column vectors. (a)ĭetermine which of the following sets are bases for R 3, considered as row vectors. (a)ĭetermine which of the following sets are bases for R 2, considered as column vectors. Note that the elements in the leading diagonal of a skew-symmetric matrix are always zero.ĭetermine which of the following sets are bases for R 2, considered as row matrices. Skew-symmetric matrix: A square matrix such that a i j = − a j i ∀ i & j.Įxample.
![matrix meaning matrix meaning](https://www.algebrapracticeproblems.com/wp-content/uploads/2020/12/example-of-2x2-commuting-matrices-300x134.png)
Symmetric matrix: A square matrix such that a i j = a j i ∀ i & j.
![matrix meaning matrix meaning](https://miro.medium.com/max/4000/0*luNBhHsLBbjMSHew.png)
Triangular matrix: A square matrix, in which all the elements below (or above) the leading diagonal are zero.Įxample: ( 3 1 4 0 2 − 1 0 0 4 ) and ( 1 0 0 2 3 0 4 − 1 5 ) are upper triangular and lower triangular matrices, respectively. Unit matrix: A diagonal matrix having all the diagonal elements equal to 1.Įxample:, , … A unit matrix is also known as an identity matrix and is denoted by the capital letter I. Scalar matrix: A diagonal matrix having all the diagonal elements equal to each other.
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5.ĭiagonal matrix: A square matrix, all of whose elements except those in the leading diagonal are zero. Example: The matrix ( 3 − 2 − 3 1 ) is a square matrix of size 2 × 2. Square matrix: A matrix having equal number of rows and columns. A null matrix is also known as a zero matrix, and it is usually denoted by 0. Null matrix: A matrix having all elements zero. 2.Ĭolumn matrix: A matrix having a single column. Row matrix: A matrix having a single row.