**Transpose**: *A*^{T}

- Algorithm:
*A*^{T}[*i*,*j*] =*A*[*j*,*i*], exchange the row and column indices. - # operations

**Scalar multiplication**:

- Precondition:
*c*is a real number. - Algorithm: , multiply each
element of
*A*by*c*. - # operations

**Addition**:

- Precondition:
*A*and*B*have the same shape. - Algorithm: (
*A*+*B*)[*i*,*j*] =*A*[*i*,*j*] +*B*[*i*,*j*], add element by element. - # operations

**Dot product** (of vectors): *u*^{T} *v*

- Preconditions:
- A row vector (
*u*^{T}) times a column vector (*v*); - Two vectors have the same size (
*n*).

- A row vector (
- Algorithm:
- # operations

**Norm** (*l ^{2}*-norm) of a vector: .

How can we express matrix subtraction in terms of these operations?