# Determinantal Loci

This article characterizes the points $$(x, y)$$ in the plane for which the determinant of a matrix of a particular form involving $$(x, y)$$ is $$0$$.  The matrices of interest have the form  $$A+xL+uM$$, where $$A$$, $$L$$, and $$M$$ are square matrices, $$L$$ and $$M$$ are of rank one, and $$L + M$$ is of rank two.

Old Node ID:
765
Author(s):
Marvin Marcus (University of California, Santa Barbara)
Publication Date:
Thursday, September 15, 2005
Original Publication Source:
College Mathematics Journal
Original Publication Date:
January, 1992
Subject(s):
Algebra and Number Theory
Linear Algebra
Topic(s):
Linear Algebra
Determinants
Geometry
Matrix Multiplication
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Publish Page:
Furnished by JSTOR:
File Content:
Rating Count:
17.00
Rating Sum:
54.00
Rating Average:
3.18
Author (old format):
Marvin Marcus
Applicable Course(s):
3.8 Linear/Matrix Algebra
Modify Date:
Wednesday, February 1, 2006