What is a matrix?

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Matrix is ​​an arrangement of numbers in rows and columns. In game math, it is often used as a tool to apply transformations to vectors rather than storing multiple coordinates at once.

2 rows 3 columns matrix

[ 1  2  3 ]
[ 4  5  6 ]

matrix addition

For matrices of the same size, elements at the same position are added.

[ 1  2 ] + [ 5  6 ] = [ 6  8  ]
[ 3  4 ]   [ 7  8 ]   [ 10 12 ]

If the number of rows and columns are different, they cannot be added because they cannot define the same position.

matrix multiplication

A ism × n, Bn × pWhenA × Bcan be calculated and the result ism × pall.

[ a b ] [ e f ]   [ ae + bg  af + bh ]
[ c d ] [ g h ] = [ ce + dg  cf + dh ]

Multiply one row of the front matrix and one column of the back matrix and add them. Unlike regular number multiplicationA × BandB × AThe results may be different or only one side may be calculated.

identity matrix

An identity matrix is ​​a matrix whose diagonal is 1 and the remainder is 0.

[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]

When multiplied by any matrix or vector, it maintains its original value. Transform can be used in its initial state with nothing applied.

Matrices is not a subject that involves memorizing the number table itself. This is an expression for combining the relationships and transformations of multiple axes into one operation and applying them in order.