Problem of the week - Find the nonsingular matrix
November 28, 2018
This problem of the week is about the inverse of a square matrix, where you should need to know some basic properties and how to calculate it.
Inverse matrices are useful for a variety of fields, such as:
- Cryptography, to decrypt a message that was encrypted by using an invertible matrix.
- Image processing, where several transformations can be expressed as matrix multiplication, and to reverse those transformation, you just need multiply by the inverse.
- Solving consistent independent systems of linear equations.
Cryptography and linear algebra
June 25, 2014
Since humans invented the written language, they have tried to share information secretly. This is basically, the objective of Cryptography, the study of the techniques to protect sensitive communications by means of data encryption and its posterior decryption. Encryption is the transformation of data into some unreadable form, so, even those who can see the encrypted data cannot understand the hidden information. Decryption is the reverse of encryption; it is the transformation of encrypted data back into some intelligible form.
Although there are different methods to encrypt and decrypt messages, we'll focus on a linear algebra based cipher, the Hill cipher, which uses a matrix as a cipher to encode a message, and it's extremely difficult to break when a large matrix is used. The receiver of the message decodes it using the inverse of the matrix.
