What is the rank of a matrix? The rank of a matrix A is the maximal number of linearly independent columns of A. This is, in turn, equal to the maximal number of linearly independent rows of a matrix. For example, let’s say A is a matrix that has 3 rows and 3 columns....
How to calculate the Euclidean distance between two matrices? Let A and B be two mxn matrices. And Ai,j and Bi,j be the element in the ith row and jth column of the matrix A and B, respectively. The Euclidean distance between these two matrices A and B is defined as:...
What is the Frobenius norm of a matrix? Let’s say A is an mxn matrix. The Frobenius norm of the matrix A is defined as: $latex ||A||_F=\sqrt{\sum_{i=1}^{m}{\sum_{j=1}^{n}{|A_{i,j}|^2}}} $ Here, Ai,j is the element in the ith row and jth column of the matrix A. In...
What is the max norm of a vector? The norm of a vector v is mathematically defined as follows: $latex L^q=||\vec{v}||_q=(\sum_{k}{|v_k|^q})^{\frac{1}{q}} $ When q=1, the vector norm is called the L1 norm or the Manhattan norm. So, the L1 norm of a vector is...
What is the L2 norm of a vector? The norm of a vector v is mathematically defined as follows: $latex L^q=||\vec{v}||_q=(\sum_{k}{|v_k|^q})^{\frac{1}{q}} $ When q=1, the vector norm is called the L1 norm or the Manhattan norm. So, the L1 norm of a vector is...
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