###### column vectors

- Each of the five column vectors in X defines a 2-element input vectors, and a row vector T defines the vector's target categories. (mathworks.com)
- The distinction between row vectors and column vectors is essential . (pdx.edu)
- Throughout, boldface is used for the row and column vectors. (wikipedia.org)
- The set of all row vectors forms a vector space called row space, similarly the set of all column vectors forms a vector space called column space. (wikipedia.org)
- The column space can be viewed as the dual space to the row space, since any linear functional on the space of column vectors can be represented uniquely as an inner product with a specific row vector. (wikipedia.org)
- To simplify writing column vectors in-line with other text, sometimes they are written as row vectors with the transpose operation applied to them. (wikipedia.org)
- dots \;x_{m}\end{bmatrix}}^{\rm {T}}} or x = [ x 1 , x 2 , … , x m ] T {\displaystyle \mathbf {x} ={\begin{bmatrix}x_{1},x_{2},\dots ,x_{m}\end{bmatrix}}^{\rm {T}}} Some authors also use the convention of writing both column vectors and row vectors as rows, but separating row vector elements with commas and column vector elements with semicolons (see alternative notation 2 in the table below). (wikipedia.org)

###### Cartesian

- When computed in orthonormal Cartesian coordinates, the returned vector field is equal to the vector field of the scalar Laplacian applied to each vector component. (wikipedia.org)

###### input vectors

- A 2-input hard limit neuron fails to properly classify 5 input vectors because they are linearly non-separable. (mathworks.com)
- The perceptron must properly classify the input vectors in X into the categories defined by T. Because the two kinds of input vectors cannot be separated by a straight line, the perceptron will not be able to do it. (mathworks.com)
- Rotational invariance - A vector quantity (such as the dot product or the cross product) is rotationally invariant if its value remains the same under a rotation of its input vectors. (sparknotes.com)

###### Tangent

- For any object moving through space, the velocity vector is tangent to the trajectory. (wikipedia.org)
- In this setting, a vector field gives a tangent vector at each point of the manifold (that is, a section of the tangent bundle to the manifold). (wikipedia.org)

###### unit vector

- Unit vector - A vector whose length is one. (sparknotes.com)

###### scalar multiplication

- Both the dot product and the cross product are rotationally invariant, while vector addition and scalar multiplication, in general, are not. (sparknotes.com)
- Vector Space - A set that is closed under addition and scalar multiplication. (sparknotes.com)

###### insertional mutagenesis

- Problems that may arise with gene transfer vectors include acute toxicity from the introduction of foreign materials, cellular and humoral immune responses directed against the transduced cells and products, as well as the potential for insertional mutagenesis by certain integrating vectors. (news-medical.net)
- citation needed] To date, four children in the French trial and one in the British trial have developed leukemia as a result of insertional mutagenesis by the retroviral vector. (wikipedia.org)

###### Angle

- The dot product of two vectors can be defined as the product of the magnitudes of the two vectors and the cosine of the angle between the two vectors. (wikipedia.org)

###### linearly

- functions create vectors with linearly spaced or logarithmically spaced elements, respectively. (pdx.edu)

###### elements of a vector

- Individual elements of a vector can be addressed with a Fortran like subscript. (pdx.edu)

###### Examples

- Examples of covariant vectors generally appear when taking a gradient of a function. (wikipedia.org)

###### MATLAB

- In MATLAB a vector is a matrix with either one row or one column. (pdx.edu)
- MATLAB vectors are used in many situations, e.g., creating x-y plots, that do not fall under the rubric of linear algebra. (pdx.edu)
- MATLAB still enforces the rules of linear algebra so paying attention to the details of vector creation and manipulation is always important. (pdx.edu)

###### depends on the coordinate system

- This representation of a vector field depends on the coordinate system, and there is a well-defined transformation law in passing from one coordinate system to the other. (wikipedia.org)

###### specificity

- Cell type specificity: Most viral vectors are engineered to infect as wide a range of cell types as possible. (wikipedia.org)

###### whereas

- In short, non-integrating vectors can facilitate persistent transgene expression in cells that do not proliferate, whereas integrating vectors represent a right choice if there is a need for stable genetic alteration in dividing cells. (news-medical.net)
- Whereas the scalar Laplacian applies to a scalar field and returns a scalar quantity, the vector Laplacian applies to a vector field, returning a vector quantity. (wikipedia.org)

###### retroviruses

- In addition, VVL is funded by NIH for the generation of vesicular stomatitis viruses as vaccine vectors for West Nile virus and simian retroviruses in collaboration with the Tulane National Primate Research Center in Covington, LA. (lsu.edu)
- Viral vectors, especially retroviruses, stably expressing marker genes such as GFP are widely used to permanently label cells to track them and their progeny, for example in xenotransplantation experiments, when cells infected in vitro are implanted into a host animal. (wikipedia.org)
- Some viral vectors, for instance gamma-retroviruses, insert their genomes at a seemingly random location on one of the host chromosomes, which can disturb the function of cellular genes and lead to cancer. (wikipedia.org)

###### viral vector

- Five classes of viral vector can be categorized in two principal groups, according to whether their genomes integrate into host cellular chromatin (lentiviruses and oncoretroviruses) or persist in the cell nucleus predominantly as extrachromosomal episomes (adenoviruses, adeno-associated viruses and herpes viruses). (news-medical.net)
- In conclusion, there is still a tremendous amount of work to be done in viral vector research. (news-medical.net)
- Low toxicity: The viral vector should have a minimal effect on the physiology of the cell it infects. (wikipedia.org)
- This is detrimental to predictability and reproducibility of the work conducted using a viral vector and is avoided in their design. (wikipedia.org)
- The cells can then be isolated easily as those that have not taken up the viral vector genes do not have antibiotic resistance and so cannot grow in a culture with antibiotics present. (wikipedia.org)

###### spatial

- Grassmann's 1840 work Theorie der Ebbe und Flut (Theory of the Ebb and Flow) was the first system of spatial analysis similar to today's system and had ideas corresponding to the cross product, scalar product and vector differentiation. (wikipedia.org)

###### projection of a vector

- Projection - The projection of a vector in a particular direction is its "shadow" along that direction. (sparknotes.com)
- The vector projection of a vector a on (or onto) a nonzero vector b (also known as the vector component or vector resolution of a in the direction of b) is the orthogonal projection of a onto a straight line parallel to b. (wikipedia.org)

###### matrix

- The matrix product of a column and a row vector gives the dyadic product of two vectors a and b, an example of the more general tensor product. (wikipedia.org)
- Continuing with row vectors, matrix transformations further reconfiguring n-space can be applied to the right of previous outputs. (wikipedia.org)
- The matrix transformations mount up to the left in this use of a column vector for input to matrix transformation. (wikipedia.org)
- That is, the matrix that transforms the vector components must be the inverse of the matrix that transforms the basis vectors. (wikipedia.org)
- one specified as a column matrix is known as a column vector. (wikipedia.org)

###### matrices

- Refer to Pre-allocating memory for vectors and matrices for a discussion of the performance issues. (pdx.edu)
- It is often used in copy operations and in the creation of vectors and matrices. (pdx.edu)

###### Transpose

- Otherwise the transpose operator is applied to the value, 5, before the vector is created. (pdx.edu)
- The technical construction uses the dual space associated with a vector space to develop the transpose of a linear map. (wikipedia.org)

###### another vector

- Once a vector has been created, it may be assigned to another vector. (pdx.edu)
- Cross product - also known as the "vector product", a binary operation on two vectors that results in another vector. (wikipedia.org)

###### viruses

- Viral vectors are usually derived from parental wild type viruses whose viral genes (essential for replication and virulence) have been replaced with the heterologous genes intended for cell manipulation. (news-medical.net)
- In vitro and clinical use of viral vectors is based on RNA and DNA viruses that differ in their genomic structures and host range. (news-medical.net)
- Like all replication-incompetent vectors and viruses, viral particles can only be constructed if missing functions are superseded. (news-medical.net)
- The two major classes of methods are those that use recombinant viruses (sometimes called biological nanoparticles or viral vectors) and those that use naked DNA or DNA complexes (non-viral methods). (wikipedia.org)
- Safety: Although viral vectors are occasionally created from pathogenic viruses, they are modified in such a way as to minimize the risk of handling them. (wikipedia.org)

###### coordinates

- For expressions of the vector Laplacian in other coordinate systems see Del in cylindrical and spherical coordinates. (wikipedia.org)
- The two polar coordinates of a point in a plane may be considered as a two dimensional vector. (wikipedia.org)

###### advantages

- There are numerous ways to actually create a vector, each one having advantages in particular situations. (pdx.edu)
- rather, each of the vectors has its own advantages, limitations and range of applications. (news-medical.net)
- Hi netters, I would like to report the availability of a set of reporter gene vectors that have some distinct advantages over those currently in use for the purpose of analysis of eukaryotic promoters & enhancers. (bio.net)

###### Plot

- Plot these vectors with PLOTPV. (mathworks.com)
- A feather plot displays vectors emanating from equally spaced points along a horizontal axis. (mathworks.com)

###### trials

- Furthermore, human trials have thus far used vectors that integrate into a relatively small percentage of cells within a target tissue. (news-medical.net)