column

Examples of column in the following topics:

• Spaces Associated with a linear system Ax = y

  • In other words the rows of $A$ have $m$ components while the columns of $A$ have $n$ components.
  • Now the column space and the nullspace are generated by $A$ .
  • What about the column space and the null space of $A^T$ ?
  • We summarize this by saying that row rank = column rank.
  • A generic $n \times m$ matrix can have more columns than rows (top), more rows than columns (bottom), or it could be square.

• What is a Matrix?

  • The size of a matrix is defined by the number of rows and columns that it contains.
  • Matrices which have a single row are called row vectors, and those which have a single column are called column vectors.
  • A matrix which has the same number of rows and columns is called a square matrix.
  • A matrix with an infinite number of rows or columns (or both) is called an infinite matrix.
  • For instance, $a_{2,1}$ represents the element at the second row and first column of a matrix A.

• Cumulative Frequency Distributions

  • However, this time, you will need to add a third column.
  • The first column should be labeled Class or Category.
  • The second column should be labeled Frequency.
  • Fill in your class limits in column one.
  • Next, start to fill in the third column.

• Victory Columns under the Nervan-Antonines

  • Standing between the libraries of the Forum of Trajan is a 128 foot tall victory column, known as the Column of Trajan.
  • A victory column was also erected for Marcus Aurelius (r. 161-180 CE).
  • This column is modeled on Trajan's column and was originally erected on the Campus Martius between the Temple of Divine Hadrian and the Temple of Divine Marcus Aurelius.
  • Despite the similar military scenes, the artistic style of the Column of Marcus Aurelius differs greatly from the Column of Trajan.
  • Detail of five registers or bands from the Column of Trajan.

• Matrix Multiplication

  • When multiplying matrices, the elements of the rows in the first matrix are multiplied with corresponding columns in the second matrix.
  • First ask: Do the number of columns in $A$ equal the number of rows in $B$?  
  • The number of columns in $A$ is $2$, and the number of rows in $B$ is also $2$, therefore a product exists.
  • Start with producing the product for the first row, first column element.  
  • Take the first row of Matrix $A$ and multiply by the first column of Matrix $B$:  The first element of $A$ times the first column element of $B$, plus the second element of $A$ times the second column element of $B$.

• What is a matrix?

  • Rectangles have sizes that are described by the number of rows of elements and columns of elements that they contain.
  • A "3 by 6" matrix has three rows and six columns; an "I by j" matrix has I rows and j columns.
  • A matrix that has only one row is called a "row vector. " A matrix that has only one column is called a "column vector.
  • But "rectangular" matrices are also used, as are row and column vectors.
  • A three dimensional matrix has rows, columns, and "levels" or "slices. " Each "slice" has the same rows and columns as each other slice.

• Temple Architecture in the Greek Archaic Period

  • Such aligned columns were referred to as columns in antis.
  • Doric columns are also noted for the presence of entasis, or bulges in the middle of the column shaft.
  • It is peripteral, with nine columns across its short ends and 18 columns along each side.
  • In this example, the temple was fronted by six columns, with 14 columns along its length.
  • Its colonnade has six columns across its width and twelve columns down its length.

• Expected counts in two-way tables

  • In general, expected counts for a two-way table may be computed using the row totals, column totals, and the table total.
  • For instance, if there was no difference between the groups, then about 70.78% of each column should be in the first row:
  • This leads us to a general formula for computing expected counts in a two-way table when we would like to test whether there is strong evidence of an association between the column variable and row variable.
  • To identify the expected count for the ith row and jth column, compute
  • Expected Count row i, col j = (row i total × column j total)/table total

• Partitioning the Sums of Squares

  • The column X has the values of the predictor variable and the column Y has the criterion variable.
  • The third column, y, contains the the differences between the column Y and the mean of Y.
  • The fourth column, y2, is simply the square of the y column.
  • The column Y' contains the predicted values of Y.
  • The column y' contains deviations of Y' from the mean of Y' and y'2 is the square of this column.

• Introduction to Elementary operations and Gaussian Elimination

  • If you have a matrix that can be derived from another matrix by a sequence of elementary operations, then the two matrices are said to be row or column equivalent.