Questions about matrices and vectors:Why does the dot product of

[okkvlt]

Questions about matrices and vectors:


Why does the dot product of a and b equal |a||b|cos(angle between a and b)

are the vectors of a matrix the columns or the rows, or can it be either?

I know a 0 determinant of a matrix means the vectors lie on top of each other, and the absolute value of a determinant is the area of the shape formed by a,b, and a+b, but what is the geometrical meaning of a negative versus a positive determinant?

Seing as the dot product of vectors has a geometrical interperetation, I am wondering what is the geometrical interperetation of matrix multiplication.

 

[JasonRox]

Questions about matrices and vectors:


Why does the dot product of a and b equal |a||b|cos(angle between a and b)

are the vectors of a matrix the columns or the rows, or can it be either?

I know a 0 determinant of a matrix means the vectors lie on top of each other, and the absolute value of a determinant is the area of the shape formed by a,b, and a+b, but what is the geometrical meaning of a negative versus a positive determinant?

Seing as the dot product of vectors has a geometrical interperetation, I am wondering what is the geometrical interperetation of matrix multiplication.

Try looking at cases where the determinant is positive and those negative. After about 3 examples, you might get an idea.

Or look at the equation |a||b|cos(angle ab), when is it negative? It is negative when cos is negative, and when is that?