Let the eigenvalue of the real symmetric matrix A symmetric matrix A be the transposition of the eigenvector corresponding to -1,1,1,-1 be (0,1,1). My dear, who will teach me!

Let the eigenvector belonging to the eigenvalue 1 be (x1, x2, x3)^T
Because real symmetric matrices belong to orthogonal eigenvectors with different eigenvalues
Therefore,(x1, x2, x3)^T is orthogonal to a1=(0,1,1)^T.
I.e. x2+x3=0.
The basic solution is: a2=(1,0,0)^T, a3=(0,1,-1)^T
Let P=(a2, a3, a1)=
1 0 0
0 1 1
0 -1 1
Then P^-1AP=diag (1,1,1).
So A = Pdiag (1,1,1) P^-1=
1 0 0
0 0 -1
0 -1 0

In the calculation of physical vector, is the direction represented by the sign directly before the physical quantity or by the sign of the calculation result? Good now both can work, which is more convenient? A concrete example is best given. In the calculation of physical vector, is the direction represented by the sign directly before the physical quantity or by the sign of the calculation result? Good now both can work, which is more convenient? It is best to give a concrete example.

On the same line, a positive direction is specified as a positive value, and then calculated.
That is to say:
1. Specify the positive direction before calculation
2. Mark the physical quantity (known quantity) involved in the calculation with a sign in the specified direction
3. Calculation
4. Look at the result, positive value represents positive direction; negative value represents negative direction

The difference between position vector, displacement, and distance? What is the difference between position vector, displacement and distance?

For example, if A is from B to C and then to D, then the speed of A is the vector, the length of all roads on A is the distance, and the distance between B and D is the displacement of A.

For example, if A is from B to C and then to D, then the speed of A is the vector, the length of all roads in A is the distance, and the distance between B and D is the displacement of A.

What is the difference between position vector and displacement Such as title

What is the relationship between displacement and the increment of position vector size

What is the difference between the increment of position vector modulus and the increment of displacement Rate V=d|r|/dt (r is vector, which is not easy to mark here), wrong, why The increment d|r| of AB position vector module is the module length of B point position vector minus the module length of A point position vector, and the module of position vector increment is |dr|, right? What is the difference between the increment of position vector modulus and the increment of displacement Rate V=d|r|/dt (r is a vector, which is not easy to mark here),, why The increment d|r| of AB position vector module is the module length of B point position vector minus the module length of A point position vector, and the module of position vector increment is |dr|, right?

There are two problems:(1) The increment of position vector film is scalar, but the increment of displacement (vector) is still vector, how can it be the same? The increment of the position vector is equal to the displacement (2) The velocity should be defined as V=|dr|/dt, i.e. the film of the increment of the position vector For example, the circular motion centered at the origin, position...

Let the eigenvalue of the real symmetric matrix A symmetric matrix A be the transposition of the eigenvector corresponding to -1,1,1,-1 be (0,1,1). My dear, who will teach me!