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3 Corrected typo.
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In the context of a mathematical definition, "such that" is a more specific version of "so". In this example:

  • Q has been defined to be any m × l matrix.
  • P has been defined to be an m × n matrix.
  • P is restricted in some way.
  • We can conclude from the restriction on P that PTP is nonsingular. In other words, "so".

Notice that the restriction on P is not explicitly stated. Instead, it is just enough of a restriction that the "so" is true. In other words, the words "such that" invert the logic. The reader must use the conclusion (that that PTP is nonsingular) to figure out what the restriction on P is.

In the context of a mathematical definition, "such that" is a more specific version of "so". In this example:

  • Q has been defined to be any m × l matrix.
  • P has been defined to be an m × n matrix.
  • P is restricted in some way.
  • We can conclude from the restriction on P that PTP is nonsingular. In other words, "so".

Notice that the restriction on P is not explicitly stated. Instead, it is just enough of a restriction that the "so" is true. In other words, the words "such that" invert the logic. The reader must use the conclusion (that that PTP is nonsingular) to figure out what the restriction on P is.

In the context of a mathematical definition, "such that" is a more specific version of "so". In this example:

  • Q has been defined to be any m × l matrix.
  • P has been defined to be an m × n matrix.
  • P is restricted in some way.
  • We can conclude from the restriction on P that PTP is nonsingular. In other words, "so".

Notice that the restriction on P is not explicitly stated. Instead, it is just enough of a restriction that the "so" is true. In other words, the words "such that" invert the logic. The reader must use the conclusion (that PTP is nonsingular) to figure out what the restriction on P is.

2 Improved formatting.
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In the context of a mathematical definition, "such that" is a more specific version of "so". In this example:

  • Q has been defined to be any m x× l matrix.
  • P has been defined to be an m x× n matrix.
  • P is restricted in some way.
  • We can conclude from the restriction on P that PTP is nonsingular. In other words, "so".

Notice that the restriction on P is not explicitly stated. Instead, it is just enough of a restriction that the "so" is true. In other words, the words "such that" invert the logic. The reader must use the conclusion (that that PTP is nonsingular) to figure out what the restriction on P is.

In the context of a mathematical definition, "such that" is a more specific version of "so". In this example:

  • Q has been defined to be any m x l matrix.
  • P has been defined to be an m x n matrix.
  • P is restricted in some way.
  • We can conclude from the restriction on P that PTP is nonsingular. In other words, "so".

Notice that the restriction on P is not explicitly stated. Instead, it is just enough of a restriction that the "so" is true. In other words, the words "such that" invert the logic. The reader must use the conclusion (that that PTP is nonsingular) to figure out what the restriction on P is.

In the context of a mathematical definition, "such that" is a more specific version of "so". In this example:

  • Q has been defined to be any m × l matrix.
  • P has been defined to be an m × n matrix.
  • P is restricted in some way.
  • We can conclude from the restriction on P that PTP is nonsingular. In other words, "so".

Notice that the restriction on P is not explicitly stated. Instead, it is just enough of a restriction that the "so" is true. In other words, the words "such that" invert the logic. The reader must use the conclusion (that that PTP is nonsingular) to figure out what the restriction on P is.

1
source | link

In the context of a mathematical definition, "such that" is a more specific version of "so". In this example:

  • Q has been defined to be any m x l matrix.
  • P has been defined to be an m x n matrix.
  • P is restricted in some way.
  • We can conclude from the restriction on P that PTP is nonsingular. In other words, "so".

Notice that the restriction on P is not explicitly stated. Instead, it is just enough of a restriction that the "so" is true. In other words, the words "such that" invert the logic. The reader must use the conclusion (that that PTP is nonsingular) to figure out what the restriction on P is.