Determinant & Eignenvalues

Question

I am looking for an intuitive meaning of:

1) Determinant of a Matrix

2) The implications of Eigenvalues and EigenVectors.

On example that really helped me from betterexplained.com

The determinant is the “size” of the output transformation. If the input was a unit vector (representing area or volume of 1), the determinant is the size of the transformed area or volume. A determinant of 0 means matrix is “destructive” and cannot be reversed (similar to multiplying by zero: information was lost).

The eigenvector and eigenvalue are the “axes” of the transformation.

Perhaps a practical example where these two concepts are applied would be really appreciated

Answer 1

The meaning of determinant had been discussed multiple times on this site. See, e.g., the following threads:

• What's an intuitive way to think about the determinant?
• What is the origin of the determinant in linear algebra?
• why determinant is volume of parallelepiped in any dimensions
• Meaning of signed volume

Answer 2

"impications" of eigenvectors /eigenvalues...for any linear function zero is a fixed point ( invariant under the function...if f is a linear function ..and..f(u) = ku ..for some number k...then the line through u and the origin (the vector subspace) is fixed under the function f.