Determinant of an Operator and of a Matrix

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Determinant of an operator. An operator is not invertible if and only if its determinant equals 0. Formula for the characteristic polynomial in terms of determinants. Determinant of a matrix. Connection between the two notions of determinant.

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This is such an elegant way of eventually getting to the determinant, whose importance was unclear to me until understanding your book/this video. I'm really glad to finally be able to interpret its meaning with regard to a transformation.

akrishna

I'm honestly flabbergasted to see such a simple definition of the determinant. The definition I remember learning is some complex algorithmic thing that requires drawing multiplying, adding and subtracting various subsets of a matrix; I remember it being very difficult to remember the correct process.

garfieldnate

Greetings Sheldon. I appreciate your book very much. If the determinant of T is defined to be the product of the eigenvalues of T, with each eigenvalue repeated according to its multiplicity, why should we take into account (-1)^n in the proposition "Determinant and characteristic polynomial". What i am understanding from the definition is that it should only be lambda_1***lambda_n (i., e the constant term of the characteristic polynomial). Ill appreciate any guidence

maxgomez

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