# Quasi Upper Triangular Matrix

## Main Question or Discussion Point

Hi, I am dealing with a 'quasi upper triangular matrix', that is mentioned in the book 'Matrix Computations' by Golub & Van Loan. However, neither in the book itself, or anywhere on the internet, am I able to find a formal definition of a 'quasi upper triangular matrix'.

I have a rough idea what this is.. an upper triangular matrix, with the odd non-zero element(s), somewhere along it's sub-diagonal. But I need an actual formal definition. Anyone furnish me with one please?

## Answers and Replies

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AlephZero
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I have a rough idea what this is.. an upper triangular matrix, with the odd non-zero element(s), somewhere along it's sub-diagonal. But I need an actual formal definition. Anyone furnish me with one please?
You probably mean "a block upper triangular matrix with either 1x1 or 2x2 blocks on the diagonal."

http://books.google.co.uk/books?id=9cwrJHFzo4cC&pg=PA98&lpg=PA98&dq=quasi+upper+triangular+matrix&source=bl&ots=Ffymx1T-uA&sig=TIz0bkbjqLM1x3YIV9abcMKlUg0&hl=en#v=onepage&q=quasi upper triangular matrix&f=false

http://reference.wolfram.com/legacy/v5_2/Built-inFunctions/AdvancedDocumentation/LinearAlgebra/LinearAlgebraInMathematica/MatrixComputations/MatrixDecompositions/AdvancedDocumentationLinearAlgebra3.4.5.html

It should be clear exactly what G&VL mean from the context in the book.

Thanks, the first link was very helpful