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Kontinuumsmechanik

What’s Einstein’s summation convention?

Einstein’s summation convention states that indices occuring twice in a product are summed.

Kontinuumsmechanik

What's a dummy index?

A dummy index is an index which occurs twice in a product and is thus summed. Dummy indexes can be relabeled arbitrarily.

Kontinuumsmechanik

What's a free index?

A free index is an index which occurs once and is thus not summed. Each term in each equation should contain the same free index.

Kontinuumsmechanik

What's the basis of a vector space?

The basis of a vector space is a set of linear independent vectors which are used to express each vector of the spanned vector space by a linear combination of those basis vectors.

Kontinuumsmechanik

What's the transpose of a matrix?

The transpose of a matrix is given by the matrix where rows and columns are interchanged.

Kontinuumsmechanik

What's the inverse of a matrix?

The inverse of a Matrix A multiplied with the Matrix itself always leads to the Identity Matrix I. The inverse of a Matrix exists iff det(A) =I= 0.

Kontinuumsmechanik

What's a degenerate eigenvalue?

A degenerate eigenvalue (i.e. a multiple coinciding root of the characteristic polynomial) is one that has more than one linearly independent eigenvector.

Kontinuumsmechanik

cumbersome in german

lästig, unhandlich, hinderlich

Kontinuumsmechanik

Condition for a transpose of a matrix?

a*Tb = b*transpose(T)a

Kontinuumsmechanik

When is a tensor called symmetric?

transpose(T) = T

Kontinuumsmechanik

When is a tensor called orthogonal?

When the transformed vectors preserve their lengths and angles.

Kontinuumsmechanik

Why do we only consider eigenvectors with length = 1 ?

If a is a eigenvector with eigenvalue lambda then p*a (p any real number) is also an eigenvector. so we are not interested in the length of the vector and make them always equal to 1.

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