\subsection{Basics}

Matrix Creation\\

\typ{In []: C = array([[1,1,2], [2,4,1], [-1,3,7]])}\\

It creates C matrix of shape 3x3\\

Shape is dimenions of given array.

In []: C.shape 

Out[]: (3, 3)

In []: shape([[1,2],[4,5],[3,0]])

Out[]: (3, 2)

\typ{In []: B = ones_like(C)} \\

B would be array of ones with the same shape and type as C.\\

\typ{In []: A = ones((3,2))} \\

A would be new array of given shape(arguments), filled with ones.\\ 

\typ{In []: I = identity(3)}\\

I would be identity matrix of shape 3x3

\subsection{Accessing Elements}

In []: C

Out[]: 

array([[ 1,  1,  2],

       [ 2,  4,  1],

       [-1,  3,  7]])

\end{lstlisting}

Two indexes seperated by ',' specifies row, column. So \kwrd{C[1,2]} gets third element of second row(indices starts from 0).

\newpage

\begin{lstlisting}

Single index implies complete row.

\subsection{Changing elements}

\subsection{Slicing}

Accessing rows with Matricies is straightforward. But If one wants to access particular Column, or want a sub-matrix, Slicing is the way to go.

\end{lstlisting}

First index(:) specifies row(':' implies all the rows) and second index(1) specifies column(second column).

\begin{lstlisting}

\end{lstlisting}

Here we get second row(1), all columns(':') of C matrix.

\newpage

\begin{lstlisting}

\end{lstlisting}

Result is sub-matrix with first and second row(endpoint is excluded), and all columns from C.

\begin{lstlisting}

\end{lstlisting}

\typ{':2'} => start from first row, till and excluding third row.

\begin{lstlisting}

\typ{'1:'} => Start from second row, till last row\\

\typ{':2'} => Start from first column, till and excluding third column.

\subsection{Striding}

Often apart from submatrix, one needs to get some mechanism to jump a step. For example, how can we have all alternate rows of a Matrix. \\

Following method will return Matrix with alternate rows.

\end{lstlisting}

\typ{C[startR:stopR:stepR,startC:stopC:stepC]} => Syntax of mentioning starting index, ending index, and step to jump.\\

In above mentioned case, \typ{'::2'} means, start from first row, till last row(both are blank), with step of 2, that is, skipping alternate row. After first row, C[startR], next row would be C[startR+stepR] and so on.

\begin{lstlisting}

\end{lstlisting}

Same as above, just that here we get matrix with each alternate column and all rows.

\begin{lstlisting}

\Section{Matrix Operations}

For a Matrix A and B of equal shapes.

In []: A*B # Element wise product

In []: dot(A,b) #Matrix multiplication