Maths

Question 1

Properties of symmetric matrix

Answer 1

1) A= Atransposed
2) has REAL and ORTHOGONAL EIGENVALUES

Question 2

When eigenvalues are orthogonal what are the properties of its matrix

Answer 2

That U has orthogonal elite values it’s an orthogonal matrix

== U transposed = inverse U

Question 3

Properties of rotation matrix

What makes it reflection

Answer 3

That 1) the Coloums and rows are orthogonal ( hence orthogonal matrix hence uT = u-1)
2) and Ross coloumbs are ORTHONORMAL so all unit
3) hence Det must be 1 or -1

If -1 = reflection

Question 4

After diagnolisation what checks can you perform (3)

Answer 4

1) that Det m = the eigenvalues multiplied
2) that the eigenvdctors fit the matrix
3) that the characteristic equation Det A- lambda I is in fact 0 for all lambda