The Hadamard Product

As inexperienced mathematicians we may have once thought that the natural definition for matrix multiplication would be entrywise multiplication, much in the same way that a young child might say, “I writed my name.” The mistake is understandable, but it still makes us cringe. Unlike poor grammar, however, entrywise matrix multiplication has reason to be studied; it has nice properties in matrix analysis and has applications in both statistics (301 [4], 140 [5]) and physics (93, 149 [5]). Here we will only expore the properties of the Hadamard product in matrix analysis.