It is all about generalizing the concepts of space and dimension.
Matrix algebra involves transformations to appropriate forms by sometimes changing the basis.
EigneValues are a very good example where the Vectors are first converted to the basis of eignevectors. The calculations with the transormation is easier since A*x=LAMBDA*x for all eignevectors. After calculations are done , the transformation is again done to the original basis.
Saturday, January 3, 2009
Modernism
Four Literary "isms" Inside Modernism
1. Whereas Realism attempted to portray external objects and events as the common or middle class man sees them in everyday life, impressionism tries to portray the psychological impressions these objects and events make on characters, emphasizing the role of individual perception and exploring the nature of the conscious and unconscious mind.
2. Whereas Realism tried to focus on these external objects and events, expressionism tried to express the inner vision, the inner emotion, or the inner spiritual reality that seem more important than the external realities of objects and events.
3. Whereas Realism focused on external objects and events as they are (verisimilitude), surrealism tried to liberate the subconscious, to see connections overlooked by the logical mind, to deny the supreme authority of rationality and so portray objects and events as they seem rather than as they are.
4. Whereas Realism tried to show the supreme importance of rationalness and reason, absurdism tried to duplicate in literature the absurd conditions of contemporary life: nameless millions dying in wars, commonplace horrors such as the Holocaust, a world in which "God is dead" cast mankind afloat in a chartless and unknowable world void of a spiritual center, the ultimate absurd circumstances in which contemporary humankind found itself.
Source : http://vc.ws.edu/engl2265/unit4/Modernism/all.htm
1. Whereas Realism attempted to portray external objects and events as the common or middle class man sees them in everyday life, impressionism tries to portray the psychological impressions these objects and events make on characters, emphasizing the role of individual perception and exploring the nature of the conscious and unconscious mind.
2. Whereas Realism tried to focus on these external objects and events, expressionism tried to express the inner vision, the inner emotion, or the inner spiritual reality that seem more important than the external realities of objects and events.
3. Whereas Realism focused on external objects and events as they are (verisimilitude), surrealism tried to liberate the subconscious, to see connections overlooked by the logical mind, to deny the supreme authority of rationality and so portray objects and events as they seem rather than as they are.
4. Whereas Realism tried to show the supreme importance of rationalness and reason, absurdism tried to duplicate in literature the absurd conditions of contemporary life: nameless millions dying in wars, commonplace horrors such as the Holocaust, a world in which "God is dead" cast mankind afloat in a chartless and unknowable world void of a spiritual center, the ultimate absurd circumstances in which contemporary humankind found itself.
Source : http://vc.ws.edu/engl2265/unit4/Modernism/all.htm
Music : Introduction
Music is an art form whose medium is sound organized in time. Common elements of music are pitch (which governs melody and harmony), rhythm (and its associated concepts tempo, meter, and articulation), dynamics, and the sonic qualities of timbre and texture. The word derives from Greek μουσική (mousike), "(art) of the Muses".[1]
The creation, performance, significance, and even the definition of music vary according to culture and social context. Music ranges from strictly organized compositions (and their recreation in performance), through improvisational music to aleatoric forms. Music can be divided into genres and subgenres, although the dividing lines and relationships between music genres are often subtle, sometimes open to individual interpretation, and occasionally controversial. Within "the arts", music may be classified as a performing art, a fine art, and auditory art.
To people in many cultures, music is inextricably intertwined into their way of life. Greek philosophers and ancient Indians defined music as tones ordered horizontally as melodies and vertically as harmonies. Common sayings such as "the harmony of the spheres" and "it is music to my ears" point to the notion that music is often ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, saying, for example, "There is no noise, only sound."[2] According to musicologist Jean-Jacques Nattiez, "the border between music and noise is always culturally defined—which implies that, even within a single society, this border does not always pass through the same place; in short, there is rarely a consensus.… By all accounts there is no single and intercultural universal concept defining what music might be, except that it is 'sound through time'.
The creation, performance, significance, and even the definition of music vary according to culture and social context. Music ranges from strictly organized compositions (and their recreation in performance), through improvisational music to aleatoric forms. Music can be divided into genres and subgenres, although the dividing lines and relationships between music genres are often subtle, sometimes open to individual interpretation, and occasionally controversial. Within "the arts", music may be classified as a performing art, a fine art, and auditory art.
To people in many cultures, music is inextricably intertwined into their way of life. Greek philosophers and ancient Indians defined music as tones ordered horizontally as melodies and vertically as harmonies. Common sayings such as "the harmony of the spheres" and "it is music to my ears" point to the notion that music is often ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, saying, for example, "There is no noise, only sound."[2] According to musicologist Jean-Jacques Nattiez, "the border between music and noise is always culturally defined—which implies that, even within a single society, this border does not always pass through the same place; in short, there is rarely a consensus.… By all accounts there is no single and intercultural universal concept defining what music might be, except that it is 'sound through time'.
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