matrix times column vector multiplication matlab

Matrix Times Column Vector Multiplication in Matlab

When working with vectors and matrices in Matlab, it's essential to understand the basics of vector operations. In this article, we'll delve into the concept of matrix times column vector multiplication, a fundamental operation in linear algebra.

Firstly, let's clarify what we mean by 'length' when referring to a vector. We might interpret length as the number of elements in the vector (e.g., a 2-element vector) or the geometric distance from the origin to the point denoted by the vector (e.g., a 5-element vector). This ambiguity is due to the multiple ways we can apply ordinary language words like 'length' or 'size' to vectors.

In Matlab, a vector is an n-tuple of numbers, where n represents the dimensionality. Geometrically, this means that a vector can be thought of as a point in an n-dimensional space or a directed magnitude running from the origin (the zero vector) to that point. Matrices and vectors are members of R^n, where R stands for the real numbers.

Now, let's move on to scalar operations. A scalar is any real number that can be used to scale vectors. Scalars include familiar operations like addition, multiplication, exponentiation, and more. In Matlab, scalars can also be complex numbers.

When multiplying a matrix by a column vector, we're performing an operation called matrix times column vector multiplication. This process involves the dot product of each row in the matrix with the corresponding element in the column vector. The result is another column vector.

In Matlab, you can perform this operation using the `*` operator or the `dot` function. For example:

```matlab

A = '1 2; 3 4'; % define a 2x2 matrix A

v = '5; 6'; % define a 2-element column vector v

result = A * v; % perform matrix times column vector multiplication

```

The output will be another 2-element column vector, representing the result of the multiplication.

In conclusion, matrix times column vector multiplication is a fundamental operation in linear algebra and Matlab. By understanding the basics of vectors, scalars, and matrix operations, you'll be better equipped to work with these concepts in your Matlab programming endeavors.

Matrix times column vector multiplication matlab