Notation Conventions

Notation

Scalars

We will use lower-case, unbolded letters to refer to scalar quantities. For example, we would refer to the scalar quantity x using the following notation.

\[x\]

Vectors

We will use lower-case, bolded letters to refer to vector quantities. For example, we would refer to the vector quantity v using the following notation.

\[\mathbf{v}\]

Vector Indexing

We will use the notation $v_i$ to refer to the i-th element of the vector $\mathbf{v}$.

Row Versus Column Vectors

When we talk about a vector, unless otherwise specified, we will be referring to a column vector (i.e., a matrix with shape $d \times 1$).

Matrices

We will use upper-case, bolded letters to refer to matrix quantities. For example, we would refer to the matrix quantity A using the following notation.

\[\mathbf{A}\]

Matrix Indexing

1. We will refer to the i-th column of the matrix $\mathbf{A}$ as $\mathbf{a}_{i}$.
2. We do not currently have a shorthand to refer to the i-th row of a matrix.
3. We will refer to the element at row $i$, column $j$ of matrix $\mathbf{A}$ as $a_{i, j}$.

Independent versus Dependent variables

We will use x to refer to independent (i.e., input) variables and y to refer to dependent (i.e., output) variables. For instance, when describing training data, we will always use x to refer to the input variables and y to refer to the output variable.