# Rank of Matrix

The rank of the matrix is defined as “Largest order of any non-vanishing minor of the matrix”. It is denoted by R(A).

Example:

Question: Find the Rank of the matrix

Define some alias to write mathematic expressions easily and it’s also easy to understand.

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# Python reduce() Function

The function reduce(function_name, seq) continually applies the function function_name() to the sequence seq. It returns a single value.

If seq = [ a1, a2, a3, … , an ], calling reduce(func, seq) works like this: At first the first two elements of seq will be applied to func, i.e. function_name(a1,a2) The list on which reduce() works looks now like this: [ function_name(a1, a2), a3, … , an ] In the next step func will be applied on the previous result and the third element of the list, i.e. func(func(a1, a2),a3) The list looks like this now: [ function_name(function_name(a1, a2),a3), … , an ] Continue like this until just one element is left and return this element as the result of reduce() We illustrate this process in the following example:

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# Python filter() Function

The function filter(function_name, list) offers an elegant way to filter out all the elements of a list, for which the function function_name returns True. The function filter(f,l) needs a function f as its first argument. f returns a Boolean value, i.e. either True or False. This function will be applied to every element of the list l. Only if f returns True will the element of the list be included in the result list.

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# Python map() Function

The advantage of the lambda operator can be seen when it is used in combination with the map() function. map() is a function with two arguments:

r = map(function_name , seq)

The first argument function_nameis the name of a function and the second a sequence (e.g. a list) seq. map() applies the function function_name to all the elements of the sequence seq. It returns a new list with the elements changed by funcfunction_name.

Function map() can be applied to more than one list. The lists have to have the same length. map() will apply its lambda function to the elements of the argument lists, i.e. it first applies to the elements with the 0th index, then to the elements with the 1st index until the n-th index is reached:

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