**Matrices in Python without Numpy: Part 1**

**Introduction**

Python is a wonderful programming language and is a welcome addition to graphing calculators such as:

* TI nSpire CX II and TI nSpire CX II CAS

* TI-84 Plus CE Python (it's become hard to find and hopefully it won't be the case in 2023)

* HP Prime

* Casio fx-CG 50

* Casio fx-9750GIII and fx-9860GIII

* Numworks

* From France: TI-83 Premium Python, TI-82 Advanced Edition Python, Casio Graph fx-35+ E II

As I understand at time, there is no numpy module for any of the calculators*.

But we want to work with matrices. So we will need to program code to allow work with matrices. Welcome to the Matrices in Python without Numpy series!

* There is a linalg module for the HP Prime.

This series will cover:

* creating matrices and other basics

* adding and multiplying matrices

* determinant and inverse of 2 x 2 and 3 x 3 matrices

* upper triangular matrices and general determinant

In this series, a single Python file is created, matrix.py. Each of the commands are going to be a separate function within a define structure. This allows matrix.py to imported into other Python scripts by **from matrix import ***.

**Entering Matrices**

Use square brackets to enter matrices:

[ [ M11, M12, M13, ... ] , [ M21, M22, M23, ... ] , [ M31, M32, M33, ... ] ]

Each row enclosing elements per column, and each row is separated by a comma. All the rows are enclosed in square brackets.

In this sense, matrices in this sense are nested lists. Call elements by:

Call a row: matrix[row]

Call the last row: matrix[-1]

Call an element: matrix[row][column]

Number of rows: len(matrix)

Number of columns: len(matrix[0])

Remember, in Python, indices start with 0 and go to row-1, column-1. We will stick with the index convention to stay consistent.

Screenshots are made using an emulator on my.numworks.com.

**Creating and Printing Matrices**

newmatrix(number of rows, number of columns).

The matrix will be filled with zeros.

Code:

**def newmatrix(r,c):**

** M = []**

** while len(M)<r:**

** M.append([])**

** while len(M[-1])<c:**

** M[-1].append(0.0)**

** return M**

identity(size)

Creates an identity matrix, a square matrix with ones in the diagonal, zeroes everywhere else. The identity matrix a fundamental matrix.

Code:

**def identity(n):**

** M = newmatrix(n,n)**

** for i in range(n):**

** M[i][i]=1.0**

** return M**

So far, we see resulting matrices in a row or scroll off the screen. Let's make it so we can see matrices as they are written.

mprint(matrix)

Prints a matrix in text form.

**def mprint(M):**

** for r in M:**

** print([x+0 for x in r])**

List comprehension is a very powerful tool in Python.

In the following examples, we will store a 3 x 3 matrix:

mat1 = [ [ 1, 2, 3 ] , [ 4, 5, 6 ] , [ 7, 8, 9 ] ]

transpose(matrix)

The transpose function flips a matrix on it's diagonal. For each element:

M^T: M(row, col) → M^T(col, row)

**def transpose(M):**

** # get numbers of rows**

** r=len(M)**

** # get number of columns**

** c=len(M[0])**

** # create transpose matrix**

** MT=newmatrix(c,r)**

** for i in range(r):**

** for j in range(c):**

** MT[j][i]=M[i][j]**

** return MT**

scalar(matrix, factor)

Next, we have scalar multiplication, multiply each element of the matrix by the factor.

**def scalar(M,s):**

** r=len(M)**

** c=len(M[0])**

** MT=newmatrix(r,c)**

** for i in range(r):**

** for j in range(c):**

** MT[i][j]=s*M[i][j]**

** return MT**

mtrace(matrix)

Finally, we have the a trace of a matrix. The trace is the sum of all the diagonals of a square matrix. If the matrix is not square, an error occurs.

**def mtrace(M):**

** r=len(M)**

** c=len(M[0])**

** MT=newmatrix(r,c)**

** if r !=c:**

** return "Not a square matrix"**

** else:**

** t=0**

** for i in range(r):**

** t+=M[i][i]**

** return t**

In Python != means not equal.

Coming in Part 2, let's add and multiply matrices.

Happy computing,

Eddie

Source:

Ives, Thom. "BASIC Linear Algebra Tools in Pure Python without Numpy or Scipy" Integrated Machine Learning & AI December 11, 2018. https://integratedmlai.com/basic-linear-algebra-tools-in-pure-python-without-numpy-or-scipy/

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