What are eigenvalues and eigenvectors? Let’s say A is a square matrix. Now, if we multiply A with a vector u, we will get another vector v. $latex A \vec{u}= \vec{v} $ The direction of the vectors u and v will be different in most cases. In other words, if we multiply...

In our previous article, we discussed QR decomposition of a matrix. We discussed that if Ais an mxn matrix with linearly independent columns, then using QR decomposition, we can express the matrix A as a product of two matrices Q and R, where Q is an orthogonal matrix...

What is QR decomposition of a matrix? Let A be a matrix with linearly independent columns. Using QR decomposition, we can express the matrix A as a product of two matrices Q and R, where Q is an orthogonal matrix and R is an upper triangular matrix. In our previous...

What is an orthogonal matrix? An orthogonal matrix is a square matrix of real numbers such that if we take any two columns or any two rows, the two rows or the two columns will be orthonormal. In other words, if we take any two columns and perform a dot product of the...

What is the inverse of a matrix? Let’s say A is an nxn square matrix and I is an identity matrix with dimension nxn. Let’s also assume B is another nxn square matrix, such that the following is true: $latex AB=BA=I $ If such a matrix B exists for a square matrix A,...