March 2021 – Linear Combinations

Representing a Quadratic Form Using a Matrix

March 18, 2021October 10, 2021greg.mayer

To motivate the use of linear algebra to study quadratic forms, consider the following problem. Does this inequality hold for all real values of $x$ and $y$? \begin{equation*} 5x^2 + 8 y ^2 – 4 xy \geq 0 \end{equation*} Were…Continue readingRepresenting a Quadratic Form Using a Matrix

Symmetric Matrices and Orthogonal Diagonalization

March 5, 2021September 18, 2021greg.mayer

Many algorithms rely on a type of matrix which are a type of matrix that is equal to its transpose. In other words, if matrix $A$ satisfies $A=A^T$, then $A$ is symmetric. Note that if a matrix is symmetric, the…Continue readingSymmetric Matrices and Orthogonal Diagonalization