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Homework Statement
It's my understanding that 2X2 and 3X3 determinats kinda measure volume...is there a general interpretaion for an nxn determinant ( in words, not formulas please)
Yes, the idea of volume generalizes in a natural way to n-dimensional space.Homework Statement
It's my understanding that 2X2 and 3X3 determinats kinda measure volume...is there a general interpretaion for an nxn determinant ( in words, not formulas please)
One key thing: if the determinant is zero, then geometrically speaking the volume of the parallelpiped is zero, meaning one or more of the dimensions of the unit cube have been "collapsed" or "flattened." This means that the image of the map has lower dimension than vector space itself. You can't "undo" this reduction of dimensionality, meaning that the map is not invertible.Thats Great! Does the determinant imply anything about the linear map that induces it?
No, the size (magnitude) of the determinant has no correlation with how close it is to being singular.Could i say the "size" of determinant express a measure of "how much" a matrix is invertable ?