# Matrix

A matrix is a two-dimensional array of numbers. Each element can be indexed by its row and column position. Thus, a 3 x 2 matrix:

## Transpose of a matrix

Swapping columns for rows in a matrix produces the transpose. Thus, the transpose of **A** is a 2 x 3 matrix:

### Matrix addition

Matrix addition is defined as element-wise summation of two matrices with the same shape. Let **A** and **B** be two *m* x *n* matrices. Their sum **C** can be written as follows:

**C**i,j = **A**i,j + **B**i,j

### Scalar multiplication

Multiplication with a scalar produces a matrix where each element is scaled ...

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