Let α be an n-dimensional nonzero column vector and E be an n-order identity matrix. It is proved that a = e - (transpose of 2 / α multiplied by α) transpose of α α is an orthogonal matrix

Let α be an n-dimensional nonzero column vector and E be an n-order identity matrix. It is proved that a = e - (transpose of 2 / α multiplied by α) transpose of α α is an orthogonal matrix

N-dimensional column vector u
Let u be an n-dimensional sequence vector, a and B be numbers, and find the
(1)[En-au(uT)][En-bu(uT)];
(2) When a takes what value, the matrix [en Au (UT)] is invertible?
Supplement: (1) en is a diagonal matrix whose main diagonal elements are all 1; (2) ut is a transpose of U

(1)
[En-au(uT)][En-bu(uT)]
=En-(a+b)u(uT)+abu(uT)u(uT)
=En+[ab(uT)u-a-b]u(uT)
(2) For any vector u
When a is 0, the matrix [en Au (UT)] is invertible

What is the dimension of a vector? The number of vectors. What does n + 1 n-dimensional vector group mean

Vector dimension is the number of vector components (x, y) is two-dimensional, (A1, A2, A3, A4, A5) is five dimensional vector
A group of N + 1 n-dimensional vectors is a group of N + 1 n-dimensional vectors put together