Spring 2027

Linear Algebra II

Linear Algebra II covers diagonalization, Jordan canonical form, inner product spaces, spectral theorem, SVD, and bilinear forms.

no offering record for this termCredits unavailable
Recorded instructors · Spring 2027 No instructors listed

Summary

1 / 7

Past student reviews · Andrei Caldararu

Past students reported missing homework solutions, promised practice tests, and clear grading guidelines. One reviewer noted that less work sometimes resulted in higher grades than more effort.

What you’ll be able to do

  • Recall and state the formal definitions of the mathematical objects and their properties used in advanced linear algebra (e.g., diagonalizable matrices, minimal polynomials, inner product spaces, and their operators, canonical forms, etc.).

  • Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., whether a matrix is diagonalizable, whether a space is an inner product space, etc.).

  • Recall and state the standard theorems of advanced linear algebra (e.g., the spectral theorem, Sylvester’s theorem, the Gram-Schmidt algorithm, etc.), and recall the arguments for these theorems and the underlying logic of their proofs.

  • Use such theorems in the context of longer arguments by examining their premises (e.g,. establishing results on canonical forms, applying algorithms to diagonalize matrices, find canonical forms, etc.).

  • Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, induction, etc.).

  • Convey arguments using English and appropriate mathematical terminology, notation and grammar.

  • Identify applications of course content in areas of modern research.

Source: UW Guide

Grade history

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average GPA
letter grades
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Prerequisites

Course map

(MATH 234 or 375), (MATH 320, 340, 341, 345, or 375), and (MATH 341, 375, 421, 467, or 521), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate)

MATH 540

This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree

Professors

Spring 2027

No instructors recorded for this selection.

Historical instructors & teaching patterns

SHAMGAR GUREVICH is recorded teaching in Spring 2019, Spring 2020, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

Recorded history may be incomplete and does not establish a future schedule.

Calendar & sections

Spring 2027

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SectionModeEnrolled / capacityWaitlist

Times are Central. Select a meeting for details; export includes recorded dates for the selected sections.

Meeting source records
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Student experience

the class

Past student reviews · Shamgar Gurevich

One student found the course poorly organized with weak explanations, while another valued the categorical approach for understanding mathematical structure rather than engineering applications.

Recent recorded grades — Spring 2024: 3.39 GPA, 69.6% A/AB (n=23 letter grades); Fall 2024: 3.44 GPA, 70.6% A/AB (n=17 letter grades); Fall 2025: 4.00 GPA, 100.0% A/AB (n=33 letter grades).

difficulty & workload

Past student reviews · Andrei Caldararu

Past students reported missing homework solutions, promised practice tests, and clear grading guidelines. One reviewer noted that less work sometimes resulted in higher grades than more effort.

Past student reviews · Shamgar Gurevich

A student found the instructor combative, noting he spent entire class periods arguing during presentations and failed to cover many syllabus topics.

Topics

  • Diagonalization, Cayley-Hamilton theorem, minimal polynomials, and Jordan canonical form.
  • Inner product spaces, Gram-Schmidt orthogonalization, self-adjoint/unitary/positive operators, spectral theorem, and SVD.
  • Bilinear and quadratic forms, norms, bounded linear operators, matrix norms, and basic multilinear algebra.

Skills

  • Argue whether mathematical objects possess specific properties or types using formal definitions.
  • State standard theorems and recall the logic of their proofs.
  • Apply theorems in longer arguments to establish results on canonical forms and apply algorithms.
  • Prove or disprove mathematical statements using direct and indirect methods, examples, and induction.
  • Convey mathematical arguments using appropriate terminology, notation, and grammar.

Grades

Latest available · Fall 2025— not enough history to project Spring 2027.

average GPA
A / AB grades
letter grades
Instructor

Grade distribution · % of letter grades

A
AB
B
BC
C
D
F

Grades over time

Through Fall 2025

More grade details Grade mix, volume & source data

Where this course fits relative to

Latest available grades · Fall 2025 · all course levels

GPA

Higher than % of other courses in this group.

Course GPAs · red marks this course’s range

letter grades

More recorded grades than % of other courses in this group.

Typical course in this group: letter grades.

About this comparison

1316 courses over the same term, each with at least 30 recorded letter grades. Cross-listed courses count once. GPA is not a measure of difficulty or teaching quality. The typical course is the median by recorded grade count; tied values are not counted as lower. Grade counts describe course scale, not unique students or typical section size.

Descriptions compare GPA with this group’s average: at least 0.20 higher or lower; otherwise close to average. Section size uses median recorded enrollment: small up to 30, mid-sized 31–99, large 100+. Lectures and discussion/lab sections are described separately.

Sources & history

UW–Madison

Catalog & offerings

Descriptions, prerequisites, and recorded course offerings.

Catalog observation history

Observations at scan time; dates do not imply when a catalog change took effect.

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Selected offering source records

No offering records for the selected term.

Raw records 
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Student reviews

Original comments behind the course and instructor summaries.

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Madgrades

Grade history

Recorded grade distributions by term, section, and instructor.

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Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
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Full model traces

Recorded model configuration, reasoning, and tool conversations.

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Model & dataset provenance 
{
  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "f646746c14b07be2b778d971507d590c7e7400777b9dca927e54202ae5a1dd1a",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}