Matrix operations Gauss Tutorial

These videos, especially number 3, explain how matrix operations work in GAUSS

1. GAUSS Basics: Intro to Matrices.
2. GAUSS Basics: Matrix Operations.
3. GAUSS Basics: Element by Element Conformability.

Here are some of the main points:

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