Application of MATLAB in Linear Algebra (4): similar matrix and quadratic form

Sometimes we need exact eigenvalues and eigenvectors , You have to use Matlab Symbol operation function of .

stay Matlab The form of creating a symbolic matrix in is very similar to that of creating a numerical matrix , Just use symbols to define functions sym.

The following describes several forms of using this function to create a symbol matrix . 

1、 Use sym Function directly creates the symbol matrix

This method is almost the same as the method of directly creating numerical matrix .

Matrix elements can be symbolic expressions , various The length of the symbolic expression can be different , Matrix elements can be separated by spaces or commas .

for example ：

x=sym('[a+sin(d),b;1/c,d]'); y=det(x)

Get y=(d*c*a+d*c*sin(d)-b)/c

2、 Convert numerical matrix into symbolic matrix

stay Matlab in , Numerical matrices cannot be directly involved in symbolic operations , Must first be converted into a symbolic matrix . 

for example ：

a=[2/3,sqrt(2);3,1] 

a= 

0.66671.4142

3.00001.0000

b=sym(a)

b=

[ 2/3, sqrt(2)]

[3,1]

3、 Indexing and modification of symbol matrix

Matlab The index and modification of the symbol matrix of is exactly the same as that of the numerical matrix .

for example ：

For the matrix in the above example b Make changes

b(2,2)='log(9)'

01

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Find an orthogonal transformation x = Py ÿ