Matrix for a set of two-dimensional vector of real or complex array ,its add, subtract, multiply and divide the operation and general mathematical computation method is slightly different ,usually in a row vector array ,but the general computing can mix .
Even so ,in the linear algebra is defined by the matrix operation in Matlab can support .Among them such as general operations ,linear equations ,eigenvalues and singular value and factorial calculations are included .
Because the array represents a collection of digital systems ,and another array operations, must according to different rules to get in in in in in in in in in in in in in in in in operation of case C = A B can provide addition ( + ) ,subtraction ( - ) ,multiplication ( * ) ,left ( / ) ,in addition to right in addition to ( / ) C = A.
a B the office for multiplication ( * ) ,power ( ) ,in addition to ( / ) ,right to left in addition to ( / ) C = A C can provide addition ( + ) ,subtraction ( - ) ,multiplication ( * ) ,power ( ) ,right in addition to ( / ) C = C B can provide addition ( + ) ,subtraction ( - ) ,multiplication ( * ) ,power ( ) ,left except ( / ) ,right except ( .
/ ) in the table show ,an operating element in front of a point and not a little of its meaning is different .In the operating element before the point is that the project and the project of the operation ,which is called the mapping mode of operation ,the two matrix of the same size .
This and the general matrix addition and subtraction of the same ,its operation only to elements of operation .A bias function is only applied to the matrix ,is not applicable to project operation .
These operators can also be applied to matrices and constant ,the latter size .2.10.1 matrixaddition and subtraction set C ,D are 3x3 squarematrix ,and C as the magic cube ,D ;456;,namely: > ;> ;C = magic ( 3)C = 81635749 2 >> ;D = ;456;D = 12345678 9C+Dand C-D respectively the results of corresponding elements mutual operation :> ;> ;C+D% corresponding elements add ans = 939710131117 11 >> ;C-D% corresponding element subtraction ans = 7 - 13- 101- 31 -7 2.
10.2matrixmultiplication is below C. * D C * D two kinds of calculation results ,the corresponding elements of the two matrix multiplication ;mathematics multiplication :> ;> ;C. * D% corresponding element multiplied ans = 82181225422872 18 >> ;C * D% matrix multiplication ans = 54698472871025469 84mathematicalmatrix multiplication represents the significance for actual problems and .
For example, a cosmetics series ,are made of three kinds of raw material mix into ,because raw material component will produce different products series .This has four kinds of products, its basic materials are as under :> > ;weight ;A = ;521;735;ans = 243%1521%2735%composition of product components products 3component 456%product 4content of thismatrix A represents four products ( four ) .
Three kinds of weight .The three components have different prices ,the prices are provided with a row vector ,i.e. :> ;> ;P = 12050100if usingvector notation ,the first product of the composition on behalf of A ( 1,:) ,namely: > ;> ;A ( 1,:) ans = 243 is theA matrix in the first column ,its cost as long as the A ( 1,:) and P multiplication ,namely A ( 1* P,:) ,the result is :> ;> ;A ( 1,:) * P ans = 740 which is representative ofproduct costs by 1, if directly calculation for 2 x( 120)+ 4x ( 50)+ 3x ( 100)= 740 andabove the A ( 1,P :) * .
The above four kinds of products ,if the component matrix A and price matrix P ,can have four kinds of products cost :> ;> ;A P ans = 74080014901330 butabove the multiplication must be aware of the matrix size with .
The result: A size ( 4x3),P ( 3x1),the size of the results obtained for ( 3x1).In other words grossistes vetement,two matrix multiplication, matrix and the second matrix of the first row of columns ,the size should be consistent .
While the results of the size should be first matrix column and second matrix in the line ,or ( 4x3)( 3x1)= ( 4x1).In general formula says :A * B = C in terms of the relationship between its elements ,can be expressed as follows :C ( ij ) = &Sigma ;a ( IK ) B ( kJ ) ,I = 1, 2,&hellip ,m ;;J = 1,2,.
P ,k = 1,2...N .The result is the C .Since the matrix size must cooperate relationship, obviously B * A does not necessarily exist ,unless it unless its size are square matrix ( such as in front of C * D example ) ,but even so ,the result is not necessarily the same .
Such as :> ;> ;D C ans = 263826718371116128 *116* Cand C shows D * D results and different .But as long as the matrix of size match, the decomposition and distribution characteristics are still exist ,such as :A * ( B+C ) = A * B A * C or ( A * B ) * C = A * ( B * C ) matrix multiplication ,there are many interesting examples .
Since the size to fit the same size ,two square matrix multiplication should never be wrong ,at least in size with no problems .If a matrix AA ,set for the magic square ( 3x3):> ;> ;AA = magic ( 3)AA = 81635749 2,> ;> ;AA AA ans = 9167676791676767 *91 >> ;AA * AA * AA ans = 1197102911491077 11251173110112211053 >> ;ans = 119710291149107711251173110112211053threepower apparently matrix AA and AA * AA * AA results for the same .
If using the eye ( 3)function generating unit matrix ,then its whether first by and by ,the result will be the same .> ;> ;I = eye ( 3)I = 10001000 1 >> ;AA I ans = 81635749 *2 >> ;I AA ans = 81635749 *2thatI as a unit matrix ,then I * A = A * I = A ,show the exchange law in this case can be established .
2.10.3 array array division of division by element division ,so the two arrays must be the same size division .For example :> ;> ;a = a = 234 >> ;b = B = 567 >/ B ;> ;a.
Ans = 0.4000 0.50000.5714 >> ;C = ;C = 1234 >> ;d = ;d = 3587 >/ D ;> ;C. Ans = 0.3333 0.40000.37500.5714this is the twoarray passes through the right except ( ./ ) operational results .
2.10.4 array .Array one element operation can also be applied to power ,but the power number must be constant ,as Pascal function of symmetric matrix as an example :> ;> ;A = Pascal ( 3)A = 11112313 6 >> ;A.
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