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>> [r, theta] = polarcoordinates(3,4) r = 5 theta = 0.9273 in Visual Studio .NET Create PDF 417 in Visual Studio .NET >> [r, theta] = polarcoordinates(3,4) r = 5 theta = 0.9273

>> [r, theta] = polarcoordinates(3,4) r = 5 theta = 0.9273 using barcode encoding for visual .net control to generate, create qr barcode image in visual .net applications. Barcodes FAQs By typing r = polarcoo QR Code 2d barcode for .NET rdinates(3,4) you can assign the rst output argument to the variable r, but you cannot get only the second output argument; typing theta = polarcoordinates(3,4) will still assign the rst output, 5, to theta..

Complex Arithmetic MATLAB does most of it .NET QR Code s computations using complex numbers, that is, num bers of the form a + bi, where i = 1 and a and b are real numbers. The complex number i is represented as i in MATLAB.

Although you may never have occasion to enter a complex number in a MATLAB session, MATLAB often produces an answer involving a complex number. For example, many polynomials with real coef cients have complex roots:. >> solve( x 2 + 2*x + 2 = 0 ) ans = [ -1+i] [ -1-i]. Both roots of this qua qr-codes for .NET dratic equation are complex numbers, expressed in terms of the number i. Some common functions also return complex values for certain values of the argument.

For example,. >> log(-1) ans = 0 + 3.1416i More on Matrices You can use MATLAB to do computations involving complex numbers by entering numbers in the form a + b*i:. >> (2 + 3*i)*(4 - i) ans = 11.0000 + 10.0000i Complex arithmetic is a powerful and valuable feature. Even if you don t intend to use complex numbers, you should be alert to the possibility of complexvalued answers when evaluating MATLAB expressions..

More on Matrices In addition to the usu al algebraic methods of combining matrices (e.g., matrix multiplication), we can also combine them element-wise.

Speci cally, if A and B are the same size, then A.*B is the element-by-element product of A and B, that is, the matrix whose i, j element is the product of the i, j elements of A and B. Likewise, A.

/B is the element-by-element quotient of A and B, and A. c is the matrix formed by raising each of the elements of A to the power c. More generally, if f is one of the built-in functions in MATLAB, or is a user-de ned function that accepts vector arguments, then f(A) is the matrix obtained by applying f element-by-element to A.

See what happens when you type sqrt(A), where A is the matrix de ned at the beginning of the Matrices section of 2. Recall that x(3) is the third element of a vector x. Likewise, A(2,3) represents the 2, 3 element of A, that is, the element in the second row and third column.

You can specify submatrices in a similar way. Typing A(2,[2 4]) yields the second and fourth elements of the second row of A. To select the second, third, and fourth elements of this row, type A(2,2:4).

The submatrix consisting of the elements in rows 2 and 3 and in columns 2, 3, and 4 is generated by A(2:3,2:4). A colon by itself denotes an entire row or column. For example, A(:,2) denotes the second column of A, and A(3,:) yields the third row of A.

MATLAB has several commands that generate special matrices. The commands zeros(n,m) and ones(n,m) produce n mmatrices of zeros and ones, respectively. Also, eye(n) represents the n n identity matrix.

. 4: Beyond the Basics Solving Linear Systems Suppose A is a nonsing VS .NET QR ular n n matrix and b is a column vector of length n. Then typing x = A\b numerically computes the unique solution to A*x = b.

Type help mldivide for more information. If either A or b is symbolic rather than numeric, then x = A\b computes the solution to A*x = b symbolically. To calculate a symbolic solution when both inputs are numeric, type x = sym(A)\b.

. Calculating Eigenvalues and Eigenvectors The eigenvalues of a s Visual Studio .NET qrcode quare matrix A are calculated with eig(A). The command [U, R] = eig(A) calculates both the eigenvalues and eigenvectors.

The eigenvalues are the diagonal elements of the diagonal matrix R, and the columns of U are the eigenvectors. Here is an example illustrating the use of eig:. >> A = [3 -2 0; 2 -2 0; 0 1 1]; >> eig (A) ans = 1 -1 2 >> [U, R] = eig(A) U = 0 -0.4082 -0.8165 0 -0.

8165 -0.4082 1.0000 0.

4082 -0.4082 R = 1 0 0 0 -1 0 0 0 2. The eigenvector in the QR Code for .NET rst column of U corresponds to the eigenvalue in the rst column of R, and so on. These are numerical values for the eigenpairs.

To get symbolically calculated eigenpairs, type [U, R] = eig(sym(A))..
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