## What do nodules on the lungs signify?

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Commonly called a “spot on the lung” or a “shadow,” a nodule is a round area that is more dense than normal lung tissue. It shows up as a white spot on a CT scan. Lung nodules are usually caused by scar tissue, a healed infection that may never have made you sick, or some irritant in the air.

**What are lung nodules made of?**

Hamartomas are the most common type of benign lung tumor and the third most common cause of solitary pulmonary nodules. These firm marble-like tumors are made up of tissue from the lung’s lining as well as tissue such as fat and cartilage. They are usually located in the periphery of the lung.

### How many lung nodules turn into cancer?

About 40 percent of pulmonary nodules turn out to be cancerous. Half of all patients treated for a cancerous pulmonary nodule live at least five years past the diagnosis. But if the nodule is one centimeter across or smaller, survival after five years rises to 80 percent.

**When are lung nodules serious?**

Lung nodules are usually about 0.2 inch (5 millimeters) to 1.2 inches (30 millimeters) in size. A larger lung nodule, such as one that’s 30 millimeters or larger, is more likely to be cancerous than is a smaller lung nodule.

## What kind of infections cause lung nodules?

Causes and Diagnoses of Lung Nodules

- Bacterial infections, such as tuberculosis and pneumonia.
- Fungal infections, such as histoplasmosis, coccidioidomycosis or aspergillosis.
- Lung cysts and abscesses.
- Small collections of normal cells, called hamartoma.
- Rheumatoid arthritis.
- Sarcoidosis.

**What is the tensor product of Hilbert spaces?**

In mathematics, and in particular functional analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert spaces is another Hilbert space. Roughly speaking, the tensor product is the metric space completion of the ordinary tensor product.

### Is the Hilbert space a symmetric monoidal category?

It is essentially the same universal property shared by all definitions of tensor products, irrespective of the spaces being tensored: this implies that any space with a tensor product is a symmetric monoidal category, and Hilbert spaces are a particular example thereof. . i = 1 , 2. {\\displaystyle i=1,2.}

**Is there a topology for Hilbert spaces with inner products?**

Since Hilbert spaces have inner products, one would like to introduce an inner product, and therefore a topology, on the tensor product that arise naturally from those of the factors. Let H1 and H2 be two Hilbert spaces with inner products

## What is the tensor product of H1 and H2?

That this inner product is the natural one is justified by the identification of scalar-valued bilinear maps on H1 × H2 and linear functionals on their vector space tensor product. Finally, take the completion under this inner product. The resulting Hilbert space is the tensor product of H1 and H2 .