PRML读书笔记——Mathematical notation

x, a vector, and all vectors are assumed to be column vectors.

M, denote matrices.

x^T, a row vcetor, T means transpose of a vector or matrix.

(w₁ , . . . , w_m ), a row vector with m elements, and the corresponding column vector is written as w = (w₁ , . . . , w_m )^T.

[a, b], is used to denote the closed interval from a to b（闭区间）.

(a, b), is used to denote the open interval from a to b（开区间）.

[a, b), is denotes an interval that includes a but excludes b.

I_M, M * M identity matrix (also known as the unit matrix)（单位矩阵）.

f[y], A functional is denoted f[y] where y(x) is some function，e.g H[y] means entroy of function y(x).

g(x) = O(f (x)) denotes that |f (x)/g(x)| is bounded as x → ∞.For instance if g(x) = 3x² + 2, then g(x) = O(x²).

E_x[f(x, y)], The expectation of a function f (x, y) with respect to a random variable x. Or E[x].

E_x[f(x)|z], conditioned on another variable z.

cov[x, y], covariance of vector x and vecotr y. Use cov[x] as a shorthand notation for cov[x, x].

p(B), to denote a distribution over the random variable B

“∝”， 表示成正比例