notations

• The symbol ℝ stands for the field (set) of real numbers.

• The symbol ∈ should be read as “belongs to the set.”

• Vectors are denoted via overhead arrows: for example, .

• ∈ ℝⁿ indicates that is a vector with n elements, each of which is a realnumber.

• Matrices are denoted via uppercase symbols: for example, A. Sometimes A_{m, n} is used to indicate a matrix with m rows and n columns.

• A ∈ ℝ^{m × n} indicates that A is a matrix with m rows and n columns, each ofwhose elements is a real number.

• Vector and matrix transformations are indicated via superscript T: for example, ^T or A^T.

• Individual elements of a vector or matrix are denoted via subscript: for example, A_ij or _i.

• ⟨,⟩ denotes the inner product of the two vectors and . For finite-dimensional vectors, this is equivalent to ^T.

• l̂ denotes a unit vector: ||l̂|| = 1.

• The symbol ∃ should be read as “there exists.”

• The symbol ∀ should be read as “for all.”