Linear Algebra Help and Definitions

Linear Algebra is deals with the study of vectors, vector spaces, systems of linear equations, and linear maps. This subject is very abstract in nature and can be used in scientific careers for the natural and the social areas. In most cases, you will need to have had a discrete mathematics course enter into this course.

This is also one of the upper level mathematics courses that is taken for students primarily majoring in a scientific area like mathematics and computer science.

When I took this course, it was pretty easy. It always depends on who is teaching the course, however, when you are given study guides and have an idea what type of questions are going to be on the test, there is no reason why you should not pass. This is more of the theory based course with no rigorous computation whatsoever.

Out of all upper level mathematics courses, I believe that linear algebra was among the easiest and most people never complained when they take this course compared to the other more rigorous math courses like abstract algebra and differential equations. In any case, you need to prepare and practice in this course because there is a lot to digest depending on your professor. This course does not have a lot of tedious computation but more mild application and theory.

Here are only a hand full of definitions that you will deal with in this subject area. This is more of an application type course but be cautious of the theory for it is easy to get confused.

Linear Algebra Help and Definitions

eigenvalues and eigenvectors – any number such that a given square matrix minus that number times the identity matrix has a zero determinant; a linear transformation that is a nonzero vector to which when that transformation is applied to it, may change in length, but not direction.

invertible matrix – is a square matrix that results in an identity matrix when multiplied by another.

isomorphism – a linear transformation in which a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

linear map – is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

positive definite – a matrix, function, function on a group, or definite bilinear form, that is a positive real number.