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Tracing of Square matrices:
The trace of a square matrix is the addition of all the elements on the diagonal. For illustration, for the preceding matrix it is 1 + 6 + 11 + 16, or 34.
The square matrix is symmetric if aij = aji for all i, j. In another words, all the values opposite to the diagonal from each other should be equal to each other. In this illustration, there are three pairs of values opposite to the diagonals, all of which are equal that is the 2's, the 9's, and the 4's.
The square matrix is a diagonal matrix if all values which are not on the diagonal are 0. The numbers on the diagonal, though, do not have to be all nonzero though often they are. Mathematically, this is written as aij = 0 for i ~= j.
An example of a diagonal matrix is shown here.
Built-in colormaps: The MATLAB has numerous built-in colormaps which are named; the reference page on colormap shows them. Calling the function colormap without passing any ar
Creating the structure Variables: Creating a structure variable can be accomplished by simply storing the values in fields by using assignment statements, or by using the stru
Interchange rows : for illustration interchanging rows ri and rj is written as
Passing Structures to Functions: The whole structure can be passed to a function, or separate fields can be passed. For illustration, here are the two distinct versions of a f
Displaying the cell arrays: There are several techniques of displaying the cell arrays. The celldisp function shows all elements of the cell array: >> celldisp(cellro
Forward elimination: In forward elimination, we want to obtain a 0 in the a 21 position. To accomplish this, we can alter the second line in the matrix by subtracting from it
Illustration of Gauss elimination: For illustration, for a 2 × 2 system, an augmented matrix be: Then, the EROs is applied to obtain the augmented matrix into an upper
Reduced Row Echelon Form: The Gauss Jordan technique results in a diagonal form; for illustration, for a 3 × 3 system: The Reduced Row Echelon Forms take this one step
Algorithm for the function e: The algorithm for the function eoption is as shown: Use the menu function to show the 4 choices. Error-check (an error would take place
Matrix solutions to systems of the linear algebraic equations: The linear algebraic equation is an equation of the form a 1 x 1 + a 2 x 2 + a 3 x 3 . . . . a n x n
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