23.02.26.md (1353B)
1 # 23/02/26 2 3 ## matrices and arrays 4 5 - a group of rows and columns, the number of rows is m, and columns is n 6 - the size of the matrix is written as (m x n), (rows, columns) 7 8 - a single row matrix is called a row vector 9 - a single column matrix is called a column vector 10 - matrix index from 1 11 - a matrix that looks like this, is the identity matrix 12 ``` 13 (1 0 0) 14 (0 1 0) 15 (0 0 1) 16 ``` 17 this can be any size, just needs to follow this shape (line from top left to bottom right 18 19 - you can only add matrices when they are the same size 20 - just add the elements from the same position into the new one 21 ``` 22 (a+b c+d ....) 23 (............) 24 ``` 25 - subtraction is the same as addition 26 27 - you can multiply matrices by numbers or other matrices 28 - we use the `.` to multiply not `x` or `*` 29 30 - when multiplying by a number, just multiply each element by the number 31 32 - when multiplying by another matrix 33 - the number of columns must be the same as the number of rows in the second matrix 34 - `{(n _ 1 == m _ 2)}` 35 - its not commutative operation (a * b != b * a) 36 - a 3 x 5 matrix can be multiplied by a 5 x 10 (the second number of the first matrix, needs to be the same as the first number of the second matrix) 37 - you multiply rows, by columns, the value at (2, 4) is the sum of the products from row 2 in matrix 1 and column 4 in matrix 2