• Archana Receives the Donna B. Hamilton Award

    Archana Khurana has been selected to receive the Donna B. Hamilton Award for Excellence in Undergraduate Teaching in a General Education Course.  Awards are based solely on student nominations and are solicited from across campus.  From the many nominations received, the selection committee was very impressed by the student experience… Read More

  • Yanir Receives a Do Good Campus Fund Grant

    Yanir’s proposal on “Incorporating outreach into the curriculum via experiential learning” is one of the only 27 projects out of 140 submissions that were funded by the UMD Do Good Campus Fund. Read More

  • Congrats to 3 CMNS Students Named Goldwater Scholars

    Congratulations to UMD’s 3 Goldwater Scholars this year, all from CMNS: Junior physics and mathematics double-degree student Yash Anand Sophomore atmospheric and oceanic science and physics double-degree student Malcolm Maas Junior biological sciences and mathematics double-degree student Jerry Shen Over the last 15 years, UMD’s nominations yielded 49 scholarships—No. 2… Read More

  • Maria Cameron Receives the 2024 MURI Award

    Congratulations to Maria Cameron for her MURI award. MURI are multidisciplinary university research initiative grants that are awarded by the department of defense. Cameron’s grant is sponsored by the office of naval research. Her team includes Balakumar Balachandran (ME) and Miao Yu (ME). This is a project on “disorder-influenced collective… Read More

  • A $27.2M Gift to the Math Department by the Brin Family

    The university announced today a big gift to the Math Department. The very generous gift of $27.2M was made by Michael & Eugenia Brin. The gift will endow the Brin Mathematics Research Center, establish an endowed chair, and launch a summer camp for high school students. The official university’s press… Read More
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Description

This course contains an abstract treatment of finite dimensional vector spaces, linear transformations and their invariants.

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and minimum grade of C- in MATH310.


Level of Rigor

Advanced


Sample Textbooks

Linear Algebra Done Right, by Sheldon Axler

Linear Algebra by Curtis


Applications



If you like this course, you might also consider the following courses

Math403

Additional Notes

Students interested in grad school in AMSC should consider this course

Students interested in grad school in MATH should strongly consider this course

Students interested in grad school in STAT should consider this course  

Topics

Review of basic Linear algebra

Abstract vector spaces

Bases and dimension

Coordinates

Subspaces

Linear transformations

Representation of transformations by matrices

Rank and nullity

Linear functionals and duality

Determinants

Definition and properties

Permutation groups

Evaluation

Decompositions

Direct sum decompositions

Invariant subspaces

Eigenvalues and eigenvectors

Characteristic and minimal polynomial

Diagonalizable operators

Primary decompositions

Rational and Jordan canonical forms

Inner Product Spaces

Orthonormal Bases

Adjoints

Positive, unitary and normal operators

The spectral theorem

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