mathematics

Thomas J. Laffey

Thomas J. Laffey is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Thomas J. Laffey rather than just read about it. In short: Thomas J. Laffey (born December 1943) is an Irish mathematician known for his contributions to group theory and matrix theory.

Key takeaways

Thomas J. Laffey belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Thomas J. Laffey to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Thomas J. Laffey from memory before moving on to harder problems.

Reference excerpt

Thomas J. Laffey (born December 1943) is an Irish mathematician known for his contributions to group theory and matrix theory. His entire career has been spent at University College Dublin (UCD), where he served two terms as head of the school of mathematics. While he formally retired in 2009, he remains active in research and publishing. The journal Linear Algebra and Its Applications had a special issue (April 2009) to mark his 65th birthday. He received the Hans Schneider Prize in 2013. In May 2019 at UCD, the International Conference on Linear Algebra and Matrix Theory held a celebration to honor Professor Laffey on his 75th birthday.

Education and career Tom Laffey was born in Cross, County Mayo. His parents were farmers, and the family had no tradition of education. His own early schooling was entirely through the Irish language, and in mathematics and physics he was more or less self-taught. The technical books he had to study were in English, which at first he found challenging. Nobody at his school had attempted honours Leaving Cert maths before. However, he got one of the highest marks in the country in the 1961 Leaving Certificate mathematics examination, thereby earning a state scholarship to university. He attended University College Galway, earning bachelor's (1964) and master's (1965) degrees in mathematical science and also winning a National University of Ireland Traveling Studentship Prize. In 1968 he was awarded the D.Phil. by the University of Sussex for a thesis on "Structure Theorems for Linear Groups" done under advisor Walter Ledermann. He immediately joined the staff at University College Dublin, from which he officially retired in 2009, but he has continued to publish regularly. His research has focussed on group theory, and later linear algebra too, and he has supervised five Ph.D. students. He has also played a significant role in the establishment of the Irish Mathematical Olympiad, and had frequently served the BT Young Scientists Exhibition as a judge and reviewer. Early in his career, he developed a strong interest in matrix theory, due to the influence of Olga Taussky-Todd, with whom he often corresponded. This was cemented by a 1972–3 sabbatical spent at Northern Illinois University.

He received the Hans Schneider Prize in 2013 in recognition of his constructive solution to the NIEP (Non-negative inverse eigenvalue problem) for non-zero spectra.

Selected publications 2018 "The Diagonalizable Nonnegative Inverse Eigenvalue Problem" (with Cronin, A.). Special Matrices, 6 (1) 273–281. 2015 "On a conjecture of Deveci and Karaduman". Linear Algebra and its Applications, Vol 471, 15 April 2015, Pages 569–574. 2012 "A constructive version of the Boyle–Handelman theorem on the spectra of nonnegative matrices". Linear Algebra Appl., Volume 436, Issue 6, 15 March 2012, pages 1701–1709. 2006 "Nonnegative realization of spectra having negative real parts" (with H. Šmigoc). Linear Algebra Appl., 416 (1) 148–159. 2004/2005 "Perturbing non-real eigenvalues of nonnegative real matrices". J. Linear Algebra, 12 73–76 (electronic). 1999 "A characterization of trace zero nonnegative 5 × 5 matrices". (with E. Meehan) Linear Algebra Appl., 302–3. 1996 "The real and the symmetric nonnegative inverse eigenvalue problems are different" (with C.R. Johnson, R. Loewy). Proc. Amer. Math. Soc, 124 (12) 3647–3651.

References

External links Thomas J. Laffey at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Thomas J. Laffey

Start with the simplest possible case. Write down what Thomas J. Laffey claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Thomas J. Laffey before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Thomas J. Laffey ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Thomas J. Laffey

In research: Thomas J. Laffey appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Thomas J. Laffey in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Thomas J. Laffey is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1943 births, 20th-century Irish mathematicians, 21st-century Irish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Thomas J. Laffey outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Thomas J. Laffey in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Thomas J. Laffey means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Thomas J. Laffey out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Thomas J. Laffey in simple terms?

Thomas J. Laffey (born December 1943) is an Irish mathematician known for his contributions to group theory and matrix theory.

Why does Thomas J. Laffey matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Thomas J. Laffey?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Thomas J. Laffey.