(number three) what are the rules of eigenvalues of symmetric matrices and how to find them? There is an example in Li Yongle's book, which says that a is a second-order matrix, and the four elements are all 1. Because a is a symmetric matrix, the eigenvalues of a are 2 and 0. How does he know the eigenvalues are 2 and 0? Is there any rule? It should not be derived from solving the eigenvalue equation? .

(number three) what are the rules of eigenvalues of symmetric matrices and how to find them? There is an example in Li Yongle's book, which says that a is a second-order matrix, and the four elements are all 1. Because a is a symmetric matrix, the eigenvalues of a are 2 and 0. How does he know the eigenvalues are 2 and 0? Is there any rule? It should not be derived from solving the eigenvalue equation? .

This one doesn't need to solve the eigenvalue equation
Because the determinant of 1 A is equal to the product of all eigenvalues
The sum of the elements on the diagonal of a is equal to the sum of all the eigenvalues
Because it is of order 2, there are only two eigenvalues
The four elements are all 1, so a = 0, by the first, so there is an eigenvalue of 0
From the second, the sum of all eigenvalues = 1 + 1 = 2, if one is known to be 0, then the other is naturally 2

Why is the eigenvalue of the matrix 40-203-2-2-22 not a real number

4 0 -2
0 3 -2
-2 -2 2
Is a real number:
-520/2581
881/255
5442/947

Let a and B be NxN real symmetric matrices and a be positive definite. Please prove that if B is also positive definite, then the eigenvalues of AB are all positive

Let PAP '= e, PABP inverse = PAP' (P inverse) 'BP inverse = (P inverse)' BP inverse, B positive definite, (P inverse) 'BP inverse is also positive definite, and its eigenvalues are all positive. AB is similar to (P inverse)' BP inverse, so its eigenvalues are all positive

If the eigenvalues of a are 1,1,0, then the eigenvalues of a + e are 2,2,1, which are all greater than 0, and a + e is a real symmetric matrix, so a + e is a positive definite matrix

The necessary and sufficient condition for a real symmetric matrix to be positive definite is that the eigenvalues of the matrix are all positive
Here, the eigenvalues of a + e are 2, 2 and 1, all greater than 0
And a + e is a real symmetric matrix, so a + e is a positive definite matrix

Given that a is a 3 * 3 matrix and the absolute value of a is equal to 3, then the absolute value of 2A ^ 2
The real symmetric matrix corresponding to quadratic form f (x, y, Z,) = x ^ 2 + y ^ 2-3xy-2yz is?

1）=2*｜A｜*｜A｜=18
2）｜1 3/2 0|
|3/2 1 -1|
|0 -1 0|

Is the number 0 multiplied by a matrix equal to a 0 matrix? Is a non-zero matrix multiplied by a 0 matrix always equal to a 0 matrix?
In addition, are 0 matrices of different orders the same

A real number k multiplied by matrix A = [a11, A12; A21, A22] is equal to matrix B,
B = [k * a11, K * A12; k * A21, K * A22]. So what you said is correct

How much is the 0 power of a and the - 1 power of a respectively
Math problem, urgent!

0 power of a = 1 power of a - 1 power of a = 1 / A

The third power of a + bi is equal to 1,

X ^ 3 = 1 find the solution of the equation (x-1) (x ^ 2 + X + 1) = 0, x = 1 or x = (- 1 + I radical 3) / 2 or x = (- 1-I radical 3) / 2 (a, b) = (1,0) (- 1 / 2, radical 3 / 2) (- 1 / 2, - radical 3 / 2) or 1 open cubic radical 1 can be expressed as cos2k π + isin2k π open cubic by complex number, K takes 0,1,2 can be cos0 + isin0 = 1 Cos2 π / 3 + isin2 π / 3 = - 1 / 2 + I radical 3 / 2 Cos4 π / 3 + isin4 π / 3 = - 1 / 2-I radical 3 / 2

Given the function f (x) = ax INX, if f (x) > 1 is constant in the interval (1, positive infinity), then the range of real number a is

A: a > = 1
Let's look at the analysis: F (x) = ax LNX, if f (x) = ax LNX > 1, it holds on (1, + OO),
The separation constant a, i.e. a > (1 + LNX) / X is constant on (1, + OO),
The problem is equivalent to a > maxh (x), where H (x) = (1 + LNX) / x, x > 1
If h (1) = 1, then it is easy to know that h (x) is continuous at x = 1,
So maxh (x) = (X -- > 1) limh (x) = H (1) = 1,
Because x > 1, so h (x) maxh (x), we get the value range of a: a > = 1
We need to understand it carefully and take the equal sign

Find the area of the graph represented by the set {(x, y), X absolute value + y absolute value less than or equal to 2}

First quadrant
x>0,y>0
x+y=2
Beta Quadrant
x0
-x+y=2
Others, and so on
So this is a square
The point of intersection with the coordinate axis is (± 2,0), (0, ± 2)
So diagonal length = 4
So area = 4 × 4 △ 2 = 8