Let a be a real symmetric matrix and IAI ＜ 0, it is proved that there exists a non-zero n-dimensional column vector x, such that the transpose ax of X

Let a be a real symmetric matrix and IAI ＜ 0, it is proved that there exists a non-zero n-dimensional column vector x, such that the transpose ax of X

It is proved that a is a real symmetric matrix,
Then there exists an orthogonal matrix P satisfying p'ap = diag (A1, A2,..., an). [p '= P ^ - 1]
Where a1, A2,..., an are the eigenvalues of A
And because | a | = A1A2... An

Suppose there is an n-dimensional vector x, then does x have an inverse quantity, or 1 / x

Only one-dimensional vector as a first-order matrix may have an inverse matrix. {a], a ≠ 0, and its inverse matrix is {1 / a}. When the dimension is greater than or equal to 2, the vector cannot be conversed