Matrix Multiplication Example Pdf
Thread index int tx threadIdx x. You can re-load this page as many times as you like and get a new set of numbers and matrices each time.
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Alternative Ways to Think about Matrix Multiplication Example.
Matrix multiplication example pdf. Also unlike number arithmetic and algebra even when the product exists the order of multiplication may have an effect on the result. 3570 multiplications and additions. Int by blockIdx y.
Lecture Example No 2 to 14 Matrix Multiplication Singular cases D are pivot positions O solution Eit 3 X y B D z O infinitely. A 1 A 2 A 3. Matrix Sequential algorithm complexity.
17354 2380 multiplications and additions to compute multiplying the result of A 1 A 2 with A 3. Log p n Why. Recalling Matrix Multiplication The product of a matrix and a matrix is a matrix given by for and.
N2p Communication complexity of all-gather. To multiply a matrix by a scalar we multiply each entry in by For example 4 Scalar Matrix BR 2 3 5 0 BR 42 43 45 40. 3 4 6 2 26 26.
17235 1190 multiplications and additions to compute A 1 A 2. N4454 3MatrixMultiplication 32 vectorwidth ThematrixmultiplicationalgorithmandtheMatrixclassasshowninListings2and 3areportabletodifferenttargetswithdifferent𝒲𝚃. Example of Matrix Multiplication Device multiplication function called by Mul Compute C A B wA is the width of A wB is the width of B __global__ void Muld float A float B int wA int wB float C Block index int bx blockIdx x.
αβA αβA αABαAαB. A matrix is a rectangular array of numbers and an m by n matrix also written rn x n has rn rows and n columns. Matrix Multiplication 72 Introduction When we wish to multiply matrices together we have to ensure that the operation is possible - and this is not always so.
The example of Matrix Multiplication to introduce the basics of GPU computing in the CUDA environment. N2 multiplying n elements of each row of the matrix times n elements of the vector Parallel algorithm computational complexity. Basic Algorithms and Notation 2.
Then ACjk AjCk for 1 j m and 1 k p. Consider the following example for multiplication by the zero matrix. Alternative Ways to Think about Matrix Multiplication Example.
Scalar by a matrix by multiplying every entry of the matrix by the scalar this is denoted by juxtaposition or with the scalar on the left. A 3 is 35x4. View Lecture 02 - complete - SU21pdf from MA 511 at Purdue University.
2 1 6 9 3 6 0 2 12 18 6 12 0 sometimes you see scalar multiplication with the scalar on the right α βA αAβA. We can also mul tiply any matrix A by a constant c and this multiplication just multiplies every entry of A by c. On this page you can see many examples of matrix multiplication.
Example 1 Matrix Equality Let A 79x 0 1 y 1 and B 790 0 111. 2 3 3 5 5 8 3410 Hf. We can add two matrices if they are the same shape and size.
All processes sending log p. Find the values of x and y such that A B. Entry of matrix product equals row times column Suppose A is an m-by-n matrix and C is an n-by-p matrix.
The goal of this module is to show the student how to o oad parallel computations to the. An Example Suppose. Multiplying matrices - examples.
Scalar Multiplication A matrix of order such as 6contains only one entryTo distinguish this matrix from the number 6 we refer to 6 as a scalar. We can multiply a number aka. In other words O is the additive identity for the set of all m n matricesFor example the following matrices are the additive identities for.
The Identity Matrix 15 Example 5 The matrices A B are A 4 3 2 5 6 3 3 5 2 and B 3 4 3 1 2 2 7 11 9. Multiplication by the Zero Matrix Compute the product A0 for the matrix A left beginarrayrr 1 2 3 4 endarray right and the 2 times 2 zero matrix given by 0 left beginarrayrr 0 0 0 0 endarray right. Let us assume that n ΘN m ΘN and k ΘN.
A 2 is 2x35. In general in our work with matrices we will refer to real numbers as scalars. It is assumed that the student is familiar with C programming but no other background is assumed.
You can also choose different size. Solution Using the rules of matrix multiplication AB 4 3 2 5 6 3 3 5 2 3 4 3 1 2 2 7 11 9 1 0 0 0 1 0 0 0 1 I. 1 then.
Solution For the two matrices to be equal we must have corresponding entries equal so x 0 a 13 b 13 y 1 11 or y 10 a 23 b 23 quick Examples Row Matrix Column Matrix and Square Matrix A matrix with a single row is called a row matrixor row vector. BA 3 4 3 1 2 2 7 11 9 4 3 2. Let us estimate the runtime complexity of Algorithm MatrixMultiply by counting the most expensive operations in the algorithm.
In this Section we pick our way through the. Calculate AB and BA. Fully the definition of the matrix multiplication.
Structure and Efficiency 3. 14 Matrix Addition and Scalar Multiplication That is if A is an m n matrix and O is the m n zero matrix consisting entirely of zeros then A O A.
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Well Multiplying A Matrix With Number Such As Two Is Very Easy This Kind Of Matrix Multiplication Is Called Matrix Multiplication Multiplication Real Numbers
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