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Flashcards on Tensors
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What are tensors?
Tensors are mathematical objects that generalize scalars, vectors, and matrices.
What is the order/rank of a tensor?
The order or rank of a tensor is the number of indices required to describe it.
What is a covariant tensor?
A covariant tensor changes sign when the coordinates are transformed using the metric tensor.
What is a contravariant tensor?
A contravariant tensor does not change sign when the coordinates are transformed using the metric tensor.
What is a tensor product?
The tensor product of two tensors generates a new tensor with a different rank.
What is the notation for a tensor?
Tensors are often represented using superscripts and subscripts on a symbol. For example, T^i_j is a rank-2 tensor.
What is the Kronecker delta?
The Kronecker delta is defined as 1 if its indices are equal, and 0 otherwise. It is often used to manipulate tensors.
What is a tensor field?
A tensor field assigns a tensor to each point in a space.
What is the difference between a tensor and a matrix?
A tensor can have an arbitrary number of indices, while a matrix has only two.
What is a symmetric tensor?
A symmetric tensor has the property that it is equal to its transpose. That is, T_{ij} = T_{ji}.
What is a skew-symmetric tensor?
A skew-symmetric tensor has the property that it is equal to the negative of its transpose. That is, T_{ij} = -T_{ji}.
What is the Levi-Civita symbol?
The Levi-Civita symbol is a tensor whose components are 1, -1, or 0, depending on the permutation of its indices.
What is the metric tensor?
The metric tensor defines the inner product of vectors and is used to raise and lower indices on tensors.
What is a tensor contraction?
A tensor contraction is an operation that sums over repeated indices in a tensor.
What is the difference between a tensor and a scalar?
A scalar is a rank-0 tensor, while a tensor has rank greater than or equal to 1.
What are tensors?
Tensors are mathematical objects that generalize scalars, vectors, and matrices.
What is the order/rank of a tensor?
The order or rank of a tensor is the number of indices required to describe it.
What is a covariant tensor?
A covariant tensor changes sign when the coordinates are transformed using the metric tensor.
What is a contravariant tensor?
A contravariant tensor does not change sign when the coordinates are transformed using the metric tensor.
What is a tensor product?
The tensor product of two tensors generates a new tensor with a different rank.
What is the notation for a tensor?
Tensors are often represented using superscripts and subscripts on a symbol. For example, T^i_j is a rank-2 tensor.
What is the Kronecker delta?
The Kronecker delta is defined as 1 if its indices are equal, and 0 otherwise. It is often used to manipulate tensors.
What is a tensor field?
A tensor field assigns a tensor to each point in a space.
What is the difference between a tensor and a matrix?
A tensor can have an arbitrary number of indices, while a matrix has only two.
What is a symmetric tensor?
A symmetric tensor has the property that it is equal to its transpose. That is, T_{ij} = T_{ji}.
What is a skew-symmetric tensor?
A skew-symmetric tensor has the property that it is equal to the negative of its transpose. That is, T_{ij} = -T_{ji}.
What is the Levi-Civita symbol?
The Levi-Civita symbol is a tensor whose components are 1, -1, or 0, depending on the permutation of its indices.
What is the metric tensor?
The metric tensor defines the inner product of vectors and is used to raise and lower indices on tensors.
What is a tensor contraction?
A tensor contraction is an operation that sums over repeated indices in a tensor.
What is the difference between a tensor and a scalar?
A scalar is a rank-0 tensor, while a tensor has rank greater than or equal to 1.
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