 # Matrix operations Gauss Tutorial

Is there a good tutorial that describes all the possible element-by-element operations and conformability in GAUSS? I understand that they are more extensive than the standard case where the matrices have to be of the same size, but I cannot find a good tutorial on the internet to understand all the possible cases.

Any help would be greatly appreciated.

0

1. A scalar is Element-by-Element (ExE) conformable with a vector or matrix of any size.
2. A vector or matrix will be ExE conformable of another vector or matrix with the same dimensions.
3. A row vector is ExE conformable with a matrix that has the same number of columns as the row vector.
4. A row vector is also ExE conformable with any column vector.
5. A column vector is ExE conformable with a matrix that has the same number of rows as the column vector.

1. Scalar with Matrix or Vector
This is pretty straightforward and probably already known.

```//Create a scalar
s = 2.5;

//Create a 2x2 matrix
x = { 4 3,
2 1 };

out = s .* x;
```
```out = 8 6
4 2
```

2. Vectors or matrices of the same size
This is also pretty straightforward and probably already known.

```//Create a 2x2
a = { 5 4,
3 9 };

//Create a 2x2 matrix
b = { 4 3,
2 1 };

out = a .* b;
```
```out = 20 12
6  9
```

3. Row Vectors with a matrix with same number of columns
Each element of the row vector, a will multiply down a column of b.

```//Create a 1x4 row vector
a = { 5 4 3 9 };

//Create a 3x4 matrix
b = { 4 3 2 7,
2 1 3 5,
10 9 8 1 };

out = a .* b;
```
```out = 20     12      6     63
10      4      9     45
50     36     24      9
```

4. Row Vector with a column vector
The column vector b will be expanded to have as many columns as the row vector, a. Then each element of a will multiply down the newly expanded columns of b.

```//Create a 1x4 row vector
a = { 5 4 3 9 };

//Create a 3x1 matrix
b = { 4,
2,
10 };

out = a .* b;
```
```out = 20     16     12     36
10      8      6     18
50     40     30     90
``` aptech

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