Introduction

B4P provides a library of powerful matrix functions. While vectors are modeled as 1-dimensional sets containing numerals, matrices are modeled as sets (rows) containing sets containing numerals (columns). Example: {{ 1, 2, 3 }, { 4, 5, 6 }} is a matrix consisting of 2 rows and 3 columns:

| 1 2 3 |
| 4 5 6 |

• mmul: Matrix multiplication
• minv: Matrix inversion
• mdiv: Matrix division
• mdet: Calculates determinant
• linear: Solves a set of linear equations (Gaussian elimination)

You may possibly be missing the functions like madd and msub for addition and subtraction. These two operations can be implmented with direct matrix mathematics using deep operators as shown below:

• Matrix addition: a[] +^^ b[]
• Matrix subtraction: a[] -^^ b[]
• Scalar multiplication: a[] *^^ b[]
• Scalar division: a[] /^^ b[]

Following functions, also described in this section, allow any types in their matrices because contents are only moved and not calculated:

• horizontal: Converts a flat or vertical matrix to a horizontal matrix (1 row, several column elements)
• vertical: Converts a flat or horizontal matrix to a vertical matrix (1 column, several row elements)
• flat: Flattens the matrix to all values arranged in a simple set
• diagonal: Creates a matrix with values along the diagonal and zero in the remaining fields
• transpose: Transposes a matrix

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Procedures and Functions Provided:

Identity Matrix:
    identity

matrix multiplication, matrix division:
    mdiv
    mmul

matrix inversion:
    minv

matrix determinant:
    mdet

linear equation:
    linear

Make matrix horizontal:
    horizontal

Make matrix vertical:
    vertical

Flatten matrix:
    flat

Put values diagonally into matrix:
    diagonal

transpose matrix:
    transpose

flip matrix:
    flip horizontally
    flip vertically

rotate matrix:
    rotate left
    rotate right
    compose matrix
    echo matrix
    print matrix