If A is triangular and no entry on the main diagonal is zero

muthuraman · May 1, 2015

A is invertible... How give me the proper explanation...

HallsofIvy · May 1, 2015

A matrix is invertible if and only if its determinant is 0. And for any triangular matrix, the determinant is simply the product of the numbers on the diagonal.

mathman · May 1, 2015

HallsofIvy said:

A matrix is invertible if and only if its determinant is 0. And for any triangular matrix, the determinant is simply the product of the numbers on the diagonal.

I presume you meant determinant is NOT zero.

HallsofIvy · May 1, 2015

mathman said:

I presume you meant determinant is NOT zero.

Yes, of course. Thank you!

mathwonk · May 8, 2015

also it should be obvious that the rows are independent. also the columns. so the map defined by the matrix is clearly injective.

If A is triangular and no entry on the main diagonal is zero

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